AlllDh 13flS7t,

I

UNITED STATES DEPARTMENT OF COMMERCE

Maurice H. Stans, Secretary

NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director

Ion-Selective Electrodes

Proceedings of a Symposium held at the

National Bureau of Standards

Gaithersburg, Maryland

January 30-31, 1969

Richard A. Durst, Editor

Institute for Materials Research

National Bureau of Standards

Washington, D.C. 20234

National Bureau of Standards Special Publication 314

Nat. Bur. Stand. (U.S.), Spec. Publ. 314, 474 pages (November 1969)

CODEN: XNBSA

Issued November 1969

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 (Order by SD Catalog No. C 13.10:314), Price $3.50
ION-SELECTIVE ELECTRODES

Richard A. Durst

Institute for Materials Research

Analytical Chemistry Division National Bureau ofStandards

Washington, D. C. 20234

ABSTRACT

This volume contains a review of ion-selective electrodes, emphasizing

the non-glass types, and provides a thorough and critical evaluation of the

subject. It consists of eleven invited review papers and selected discussions from the Symposium on Ion-Selective Electrodes held at NBS on

January 30-31, 1969. This publication provides a comprehensive survey

of the field and should prove very valuable in advancing the state of the

art. The chapters include discussions on the theory, characteristics, and

methodology of all types of ion-selective electrodes; their use in ther- modynamic, kinetic, and complex-ion studies; standards; pure and applied research in various biomedical areas of interest; industrial analysis

and control systems; and applications to diverse analytical problems.

Both the present status and future potential of these sensors are discussed

in a wide range of scientific disciplines, from the physical sciences to biomedicine. Extensive bibliographies provide an excellent survey of the

literature for anyone using or anticipating the use of these electrodes. Key words; Ion-selective electrodes; specific-ion electrodes; review of

ion-selective electrodes; symposium proceedings.

Library of Congress Catalog Card Number: 79-601302

ii
FOREWORD

The Analytical Chemistry Division of the NBS Institute for Materials

Research provides a major national focal point for analytical chemistry

through its continuing efforts to encourage meaningful analytical measurements, to exercise leadership in attacking analytical problems of the

nation, and to fill in gaps in critical measurement competences. This Division consists at present of about 120 technical personnel encompassing some 57 different analytical competences from activation analysis and

atomic absorption to vacuum fusion and x-ray spectroscopy. These competences are charged with the responsibility for research at the forefront

of analysis, as well as for an awareness of the practical sample be it Stan- dard Reference Material or service analysis.

One important mechanism by which the Division exercises leadership

in the "state of the art" of a competence is that of sponsoring special conferences and symposia. Experts from around the world are invited to these conferences to summarize the present status of the many facets of

a particular competence. In addition, contributed papers as well as comments of rapporteurs or summaries of panel discussions are often used to help better define this status. The first such conference sponsored by the Division was a broad one on

'Trace Characterization — Chemical and Physical" held October 3-7,

1966 at the new NBS Laboratories at Gaithersburg, Maryland. On June

12-13, 1967 a seminar on a more restricted topic, ''Quantitative Electron

Probe Microanalysis," was held in these same facilities and on October

7-11, 1968 the Division hosted the 1968 International Conference on "Modern Trends in Activation Analysis." The hard-cover proceedings of

each of these meetings are available from the Government Printing Office

as NBS Monograph 100, NBS Special Publication 298 and NBS Special

Publication 3 1 2 respectively.

As a continuation of these definitive "state of the art" conferences, the

Analytical Chemistry Division and the NBS Institute for Materials

Research were very pleased to host the Symposium on Ion-Selective

Electrodes. The interest shown in this Symposium clearly demonstrated

the breadth and vitality of this subject. Over 450 scientists representing

a broad spectrum of industrial, governmental, and educational institutions attended. The format of the symposium provided an excellent opportunity

for dialogue between specialists of varying backgrounds and interests. This volume contains the invited papers presented at the Symposium,

together with summaries of selected segments of the discussion sessions.

Those interested in recent innovations in the area of quantitative elec- troanalytical chemistry will find this book on the non-glass ion-selective

electrodes to be a very comprehensive source of information.

iii
iv ION-SELECTIVE ELECTRODES

Particular thanks are due Richard A. Durst for his vision in perceiving

the need for this symposium, and for his tireless efforts as Chairman and

Editor in carrying this vision through to reality.

W. Wayne Meinke, Chief

Analytical Chemistry Division
PREFACE

This book is the formal report of the proceedings of the Symposium on

Ion-Selective Electrodes sponsored by the Analytical Chemistry Division of the NBS Institute for Materials Research. The purpose of this meeting was to survey and evaluate the recent advances in the theory,

development, and application of the non-glass types of ion-selective elec- trodes, and to provide the specialist and novice alike with a comprehensive review of the "state of the art" of these new electrochemical sensors. This volume consists of the texts of the invited lectures, including additional material not presented at the symposium, and selected segments

of the extensive (more than 2 1/2 hours) discussion sessions. The authors

have discussed various aspects of the present and future capabilities of

these electrodes, with emphasis placed on the applications and methodology in a wide variety of scientific disciplines. It is felt that the topics

presented provide as broad a coverage of the interdisciplinary aspects

of these electrodes as is feasible at this stage of their development.

Editorial changes have been made to achieve some measure of consistency of nomenclature both internally and with regard to the presently

accepted international system of units (SI). However. I have endeavored

to keep editorial changes to a minimum, especially with regard to content,

in order to conserve the originality of the contributions. Consequently,

certain fundamental discussions appear in more than one chapter, but in view of the diversity of approaches to this type of material, this duplication was intentionally preserved.

Typical of any new discipline, a multiplicity of terms has spontaneously

appeared relating to the novel features of this technique. Normally, a slow

and informal process of selection results in the acceptance of the ''best" nomenclature. In order to accelerate this process with respect to two important terms, I should like to take advantage of an editor's prerogative to recommend the use of ion-selective and selectivity ratio for future adoption by scientists, manufacturers, and all other pertinent organizations.

The term ion-selective does not imply sensitivity to one particular ion to the exclusion of all others as I feel the term ion-specific connotes. Although this fact of non-specificity is generally recognized by most

scientists in the field, the term ion-specific may be misleading and serves no useful purpose. The term selectivity ratio (or parameter) is strongly

recommended over the misnomer selectivity constant, since these values

are now known to be dependent on the concentration and composition of

the system. However, since I make these recommendations ''uni- laterally," I have not taken the liberty in this volume of editorially changV
vi ION-SELECTIVE ELECTRODES

ing the terms preferred by the individual authors, although I strongly sug- gest the acceptance and use of the recommended terms.

In order to specify the procedures adequately, it has been necessary to

identify commercial materials and equipment in this book. In no case does such identification imply recommendation or endorsement by the

National Bureau of Standards, nor does it imply that the material or equipment is necessarily the best available for the purpose.

An undertaking of the magnitude of the symposium and this book

would not have been possible without the cooperation and assistance of a large group of people within the Analytical Chemistry Division and the

National Bureau of Standards. Many of these individuals served on nu- merous committees and assisted during the symposium in various capacities. Particular thanks are given to Dr. W. Wayne Meinke, Dr. Roger

G. Bates, and Dr. John K. Taylor who guided me through the complicated

initial stages of organizing the symposium and for their subsequent support in preparing this book. The NBS Office of Technical Information

and Publications under the direction of W. R. Tilley, with special help

from Robert T. Cook, Rubin Wagner, and Mrs. Rebecca Morehouse,

gave invaluable assistance in many phases of the effort, varying from the

initial publicity brochures and program to this final computer-assisted

printing and publication of the proceedings. Within the Analytical Chemistry Division, special thanks are given to Mrs. Carolyn Smith and Mrs.

Jean Gossard for their continuous effort in typing the coded manuscripts

and other material, to Mrs. Joy Shoemaker and Robert Boreni for pre- paring the many tables and figures, and to my wife, Susan, for her help

in the tedious task of indexing. Particular appreciation is expressed to Mrs. Rosemary Maddock who provided coordination and editorial assistance in the many phases of preparing this book.

April 15, 1969 Richard A. Durst
CONTENTS

Page Abstract ii Foreword iii Preface v Contents vii Authors Chapter 1. THEORY OF MEMBRANE ELECTRODE POTENTIALS: AN EXAMINATION OF THE PARAMETERS DETERMINING THE SELECTIVITY OF SOLID AND LIQUID ION

EXCHANGERS AND OF NEUTRAL ION-SEQUESTERING

MOLECULES

by George Eisenman

Introduction 1 Solid Ion Exchangers {e.g., The Glass Electrode) 2 Liquid Ion Exchangers 4

Limiting Case of Complete Dissociation 5 Limiting Case of Strong Association 5 Neutral Sequestering Agents Which Act as Molecular Carriers of Ions 7 Membrane Potential 8 The Factors Determining Selectivity for Each of These Types of Membranes 10

Solid Ion Exchangers 10 Liquid Ion Exchangers 16 Neutral Carriers 21 Summary 26 The Origin of Equilibrium Specificity 27

Free Energy and Equilibrium Specificity 27

Ion Exchangers 28

Neutral Sequestering Molecules 32

Practical Considerations 36 Appendix— Derivation of the Equations for the Membrane Potential at Zero

Current 37

Solid Ion Exchanger Membranes 37

Liquid Ion Exchanger Membranes 42

Neutral Carriers 5

1

Acknowledgment 54

References 54 Chapter 2. SOLID-STATE AND LIQUID MEMBRANE IONSELECTIVE ELECTRODES

by James W. Ross, Jr.

Introduction 57 The Practical Importance of Ion Activity Measurement 57 The Ideal Nernst Electrode 58 Advantages and Disadvantages of Electrode Methods 60

Liquid Membrane Systems 61 General Properties 61 Phosphate Ester Systems 65 Other Cation-Selective Liquid Systems 71

vii
^Ijj ION-SELECTIVE ELECTRODES

Anion-Selective Liquid Systems 72

Solid-State Membrane Systems 73 General Properties 73 Rare-Earth Fluoride Membranes 75 Systems Based on Silver Sulfide 77 Mixed AgaS-AgX Systems 78 Mixed Silver Sulfide-Metal Sulfide Membrane Systems 79

Interferences at Solid-State Membrane Electrodes 81 Future Developments 86

References 88 Chapter 3. HETEROGENEOUS MEMBRANE ELECTRODES

by Arthur K. Covington

Introduction 89 The Development of Heterogeneous Membrane Electrodes 89 Ion-Exchange Resins 90

Precipitate Type 90

Other Materials 94

Properties of the Most Useful Electrode Systems 94

Preparation 94

Silver Halide Electrodes 95

Sulfate and Phosphate Electrodes 101

Sulfide Electrode 101 Fluoride Electrode 102

Theoretical Considerations 104 Acknowledgment 105 References 105 Chapter 4. REFERENCE ELECTRODES

by Arthur K. Covington

Introduction 107

Classification of Reference Electrodes and Their Usage 108

Internal Reference Electrodes for lon-Selecfive Electrodes 109 Use of Reference Electrodes for Direct Comparison with an Ion-Selective Electrode Supposedly Reversible to the Same Ionic Species 1 10 Use of Reference Electrodes Reversible to Another Ion; Often That of an Added "Inert" Electrolyte 1 10 Use of Reference Electrodes as "Bridging" Electrodes 1 1

1

Use of Reference Electrodes of (Ideally) Invariant Potential 1 12 Use of a Second Similar Ion-Selective Electrode as a Reference Electrode 1 13 Preparation and Properties of Some Important Reference Electrodes 1 14 The Hydrogen Gas Electrode 1 14

Silver-Silver Halide Electrodes 1 15 The Mercury-Mercurous Chloride (Calomel) Electrode 1 18 Mercury-Mercurous Sulfate Electrode 122 Mercury-Mercurous Carboxylate Electrodes 123 Thallium Amalgam-Thallous Chloride Electrode 124

Liquid Junction Potentials 127 Temperature Effects 136 References 138
CONTENTS ix Chapter 5. THERMODYNAMIC STUDIES

by James N. Butler

Introduction 143 The Lanthanum Fluoride Electrode 148

Selectivity 149

Stability and Kinetic Response 154

Acidity Effects 156

Deviations from the Nernst Equation 158

Equilibria 163

Activity Coefficient Measurements 171 Kinetics 174 Non-Aqueous Solutions 176 The Silver Sulfide Membrane Electrode 177

Miscellaneous Solid-State Electrodes 180

Calcium-Selective Electrodes 1 80

Miscellaneous Liquid Ion Exchange Electrodes 185 Conclusions 186 Acknowledgments 187 References 187 Chapter 6. ACTIVITY STANDARDS FOR ION-SELECTIVE

ELECTRODES

by Roger G. Bates and Marinas Alfenaar

Introduction. Electrode Response and Ionic Activity 191 Operational Definition of the pA Value 193 The Residual Liquid-Junction Potential. 194 Performance Tests for Ion-Selective Electrodes 195 Conventional Activity Scales 196 The pH Convention 196 Comparison of Reasonable Conventions 197

Self-Consistent Scales of Ionic Activity 199

Standard Reference Solutions 201 Comparison of Experimental and Defined pA Values 202

Chloride-Selective Electrodes 203

Sodium-Selective Electrode 205

Calcium-Selective Electrode 206

Fluoride-Selective Electrode 208

Limitations of Practical pA Measurements 210 Acknowledgment 214

References 214 Chapter 7. STUDIES WITH ION-EXCHANGE CALCIUM ELECTRODES IN BIOLOGICAL FLUIDS: SOME APPLICATIONS

IN BIOMEDICAL RESEARCH AND CLINICAL MEDICINE

by Edward W. Moore

Introduction 215

Physiologic Importance of Calcium 216 Some Historical Notes 216

Interest in Serum Ionized Calcium 217

1
X ION-SELECTIVE ELECTRODES

Electrode Characteristics and Analytical Techniques 219

Static-Type Electrode 219

Flow-Through Electrode 221

Electrode Selectivity 222

Electrode Calibration 224

Ultrafiltration and Other Methods 226

Results in Normal Subjects 228 Do Ca++ Electrodes Work in Biologic Fluids? 228 Serum Ionized vs. Total Calcium 230 pH Effects on Ionized Calcium 234 Components of Serum Total Calcium 234

Diffusible Calcium Complexes [CaR] of Normal Serum 237 Whole Blood Ca++ 239

Calcium-Heparin Complex 240 Accuracy of Electrode Measurements 241

Studies of Calcium-Binding by Normal Serum Proteins 243

[CaProt] v5."[Ca] 243 Calcium Fractions of Serum 243

Predicted vs. Observed Serum [Ca++] 244

Dissociation Constant of Calcium-Albuminate 244

Distribution of Calcium Across the Blood-CSF Barrier 247

Previous Concepts 248 Ca++ Electrode Studies in Man and Dog 249

Studies of Hyperparathyroidism 251

Studies of Serum Calcium in Cirrhosis 253 Calcium Fractions of Serum 254 Serum Proteins 257

Relation of [Ca++] to Total Calcium and Albumin 257

Relation of [CaProt] to Serum Proteins 259

Relation of Total Calcium to [CaProt] and [Alb] 261 pH Effects: Nomograms for [CaProt] 261 Summary 268

Studies of the Hypercalcemia of Cancer 269 Calcium Fractions of Serum 269

Total Calcium, Ultrafiltrable Calcium and [CaProt] 269

[Ca++] and [CaR] 270

Relative Values for [Ca++], [CaProt] and [CaR] 270 Serum Proteins 271

Relation of [Ca++] to Serum [Alb] and [Ca] 273

Relation of Total Calcium to [Alb] and [CaProt] 274

Fractionation of [CaProt] 276 Summary 281 Summary 282 Acknowledgment 283

References 283 Chapters. ION-SELECTIVE ELECTRODES IN BIOMEDICAL

RESEARCH

hy Raja N. Khuri

Potentiometry in Biological Systems.

Mixed Electrolyte Solutions 287

287
CONTENTS XI

Colloidal Solutions 289 The Liquid Junction Potential 290

Biologic Standards 292

"Bioelectrodes" 293

In Vitro vs. In Vivo 293

Potentiometric Measurements In Vitro 294

Potentiometric Measurements In Vivo 294

Extracellular Analyses 295

Intracellular Analyses 296

Biomedical Applications 298

Glass Electrodes 298 Hydrogen Glass Electrodes 299 Sodium Glass Electrodes 303

Potassium Glass Electrodes 304 Non-Glass Electrodes 306

Metallic Electrodes 306

Oxidation-Reduction Electrodes 307 Ion-Exchange Membrane Electrodes 307

Solid-State Membranes 308

Liquid-Liquid Membrane Electrodes 309

References 310 Chapter 9. ANALYTICAL STUDIES ON ION-SELECTIVE

MEMBRANE ELECTRODES

by Garry A. Rechnitz

Introduction 313

Principles 313 Complexes 317

Kinetics 330

Analysis 340

References 347 Chapter 10. INDUSTRIAL ANALYSIS AND CONTROL WITH

ION-SELECTIVE ELECTRODES

by Truman S. Light

Introduction 349

Ion-Selective Electrodes : 349

Nernst Equation and Modifications 353

Selectivity Coefficient 353 Temperature Coefficients 354 Accuracy 355

Activity and Concentration 357

Free and Total Ion Concentration 357 High Ionic Strength Medium 358

Industrial Modes for Using Ion-Selective Electrodes 359

References 373
xii ION-SELECTIVE ELECTRODES

Chapter 11. ANALYTICAL TECHNIQUES AND APPLICATIONS

OF ION-SELECTIVE ELECTRODES

by Richard A. Durst

Introduction 375

Direct Potentiometry 375 The Nernst Equation 375

Concentration Cell Techniques 376

Cahbration Curves 379

Electrode Calibration 380

Addition Techniques 381

Potentiometric Titrations 385

Applications 388

Fluoride 389

Calcium 394

Nitrate 397

Tetrafluoroborate (Boron) 398

Perchlorate..." 399

Halides 399

Cyanide 401

Silver Sulfide 402

Divalent Cations (Magnesium) 406 Copper (Cupric Ion) 407 Lead and Cadmium 407

Sulfate and Phosphate 408

Thiocyanate 408

Miscellaneous 408

Conclusion 410 Addendum— Supplementary References 410

General Applications 410

Fluoride 411 Calcium 411

Nitrate 412

Halides 412

Silver Sulfide 413

References 413 Chapter 12. SYMPOSIUM DISCUSSION 415

Index 437
AUTHORS

George Eisenman attended Harvard College and Harvard Medical

School graduating from the former summa cum laude in 1949 with an A.B. in Biology and graduating from the latter magna cum laude in 1953

with an M.D. He was elected to Phi Beta Kappa (Senior Sixteen) in 1 948

and to Alpha Omega Alpha in 1952. He was a National Scholar at Harvard Medical School from 1949-53 and received the Maimonides Award

of Harvard Medical School in 1953. He was elected to the American

Physiological Society in 1954 and nominated for the Council of the

Biophysical Society in 1966.

He was a Research Fellow of Harvard University in 1950, 1953-55;

and a Research Associate from 1955-56. In 1956, he was appointed as Permanent Senior Staff Scientist in the Department of Basic Research of

Eastern Pennsylvania Psychiatric Institute where he remained until 1962,

leaving to become Associate Professor of Physiology at the University of

Utah College of Medicine. In 1965, he joined the faculty of the University of Chicago as Professor of Physiology where he was also appointed

Professor of Biophysics in 1967. In 1969, he became Professor in the

Physiology Department at the University of California, Los Angeles. Dr. Eisenman has been visiting Professor at the Institute of Physics of the

University of Genoa, Italy, during the summers of 1963 and 1964. He is a Consultant for the Corning Glass Works and for E. I. du Pont de

Nemours Co.

His special research interest is in the mechanism by which ions and

other solutes cross biological membranes. By working with simple cations

and reducing biologic phenomena to a physical substrate, he has been

developing theories of ion permeation through non-living membranes of

sufficient structural complexity to approach the complexity conceivable

in biological systems. He hopes that his research will contribute suffixiii
xiv ION-SELECTIVE ELECTRODES

ciently to the understanding of ion permeation to help eventually in deducing the as yet unidentified mechanism (or mechanisms) by which

ions cross biological membranes.

James W. Ross was born in Ft. Lewis, Washington in 1 928. In 1951, he

received an A.B. degree in Chemistry from the University of California at Berkeley, followed by a three-year period during which he worked as a chemist for the Tidewater Associated Oil Company. In 1957, he received

a Ph.D degree in chemistry from the University of Wisconsin. He joined

the chemistry faculty of the Massachusetts Institute of Technology as in- structor in 1957, becoming Assistant Professor in 1959. In 1962, he left M.I.T. to become one of the founders of Orion Research Incorporated

where he is presently serving as Vice President and Director of Research.

Dr. Ross is the author and co-author of numerous papers and patents

in the areas of analytical chemistry and electrochemistry.

For the past several years, Dr. Ross and his research group have been

working to develop specific sensing electrodes for use in chemical analysis and process control.
Arthur K. Covington graduated with First Class Honors from the

University of Reading, England in 1953. He remained in Professor E. A. Guggenheim's department at Reading to work with Dr. J. E. Prue on the use of the glass electrode for precise thermodynamic measurements,

receiving his Ph.D. in 1956. After a period in industry, he was in 1 958 ap- pointed Lecturer in the Chemistry Department, King's College, University of Durham, which later became the University of Newcastle upon

Tyne. He was promoted to Senior Lecturer in 1967. While continuing his interest in glass electrodes, he has under Professor Lord Wynne-Jones'

encouragement, broadened his interests to include investigation of

reference electrode systems and of the properties of electrolyte solutions

by thermodynamic and spectroscopic techniques. In 1965-66, he spent

five months, while on sabbatical leave, in the Electrochemical Analysis

Section oftheNBS.

Dr. Covington is a Fellow of the Royal Institute of Chemistry and of

the Chemical Society (London), and a member of the Faraday Society.

He represents the Chemical Society on the British Standards Institution

Committees on Glass Electrodes and pH Meters.
xvi ION-SELECTIVE ELECTRODES

James N. Butler received a B.Sc. in Chemistry from Rensselaer

Polytechnic Institute (1955) and a Ph.D. in Chemical Physics from Harvard University (1959). While at Harvard he was awarded research fel- lowships from the National Science Foundation and the General Electric

Company for his doctoral studies in gas-phase reaction kinetics. These

were conducted under the direction of Prof. G. B. Kistiakowsky.

He was on the faculty of the University of British Columbia from 1959

until 1963 when he joined Tyco Laboratories, Inc., as a Senior Scientist

in Chemical Physics. In 1966, he was appointed Head of the Physical

Chemistry Department.

Dr. Butler's general research interests are in chemical kinetics and ther- modynamics; he is presently concentrating on studies of electrode

kinetics and the thermodynamics of electrolyte solutions.

He is a member of the A. A. A. S., The New York Academy of Sciences,

the American Chemical Society, the Faraday Society, and the Electrochemical Society. In 1967, he was appointed to the executive committee of the Boston Section, Electrochemical Society. Dr. Butler is the

author of five books and more than fifty scientific papers.
xvii

Roger G. Bates is chief of the Electrochemical Analysis Section of the

NBS. He was graduated from the University of Massachusetts and

received his Ph.D. degree from Duke University in 1937. Following grad- uate study, he was awarded the Sterling Fellowship at Yale University

and spent two years in research under the supervision of Professor H. S. Harned. He has been a member of the staff of the NBS since 1939 with

the exception of two periods of study abroad. He spent the academic year

1953-54 in the laboratory of Professor G. Schwarzenbach in Zurich and

studied for shorter periods in Paris and Oxford in 1 962. Dr. Bates has published about 160 technical articles. He is the author

of the book ''Determination of pH, Theory and Practice" and has contributed to many encyclopedias and monographs. He has also lectured

widely in this country on the subject of acidity measurement and in 1959 was a Swiss-American Foundation lecturer in Basel and Zurich. His studies of electrolytic solutions and the standardization of pH brought him

the Hillebrand Prize for 1955 of the Washington Section ACS and the

gold medal for exceptional service of the Department of Commerce in 1957.

Since 1 95 1 , Dr. Bates has been active in both the Analytical Chemistry

Division and the Physical Chemistry Division of the International Union

of Pure and Applied Chemistry. He served a six-year term as president of

the lUPAC Commission on Electrochemical Data and is a titular member of the Commission on Electrochemistry and the Commission on

Symbols, Terminology, and Units at the present time, as well as of the

U. S. National Committee for lUPAC.

Dr. Bates is a member of the editorial advisory boards of Analytical

Chemistry and Analytica Chimica Acta. He is a member of the ACS

council, representing the Division of Analytical Chemistry, and was the

editor of the Capital Chemist in its first year of publication. He is also a member of the Washington Academy of Sciences, Phi Beta Kappa,
xviii ION-SELECTIVE ELECTRODES

Sigma Xi, Phi Kappa Phi, and the Cosmos Club and is a fellow of the

American Institute of Chemists. His selection to receive the 1969 ACS

Award in Analytical Chemistry was recently announced.

Edward W. Moore was born in Madisonville, Kentucky on July 6,

1930, received his B.A. in Chemistry from Vanderbilt University in 1952

and his M.D. from Vanderbilt University Medical School in 1955. From

1955 to 1956, he interned in the Harvard Medical Services, Boston City

Hospital, then received a year of residency training in internal medicine

at the Lemuel Shattuck Hospital, during which time he worked on insulin

metaboHsm in diabetes. From 1957 to 1959, he was a CHnical Associate

at the National Cancer Institute in Bethesda, Md., working on several

problems in cancer and leukemia, including studies of the central nervous system in acute leukemia and studies of the physiology and pharmacology

of the blood-CSF barrier. Returning to Boston in 1959, another year was

spent in the Harvard Medical Services at Boston City Hospital. In 1960,

Dr. Moore began full-time research at the Lemuel Shattuck Hospital

where he has remained up to the present time. He has been a U.S. Public

Health Service Research Fellow, Fellow of The Medical Foundation of

Boston and Research Career Development Awardee of The National Institute of General Medical Sciences.

His major interests are electrolyte metabolism and gastrointestinal

physiology, with particular emphasis in physical chemistry and mathematical models. Over 60 works have been published in these and related

areas. Dr. Moore is a member of numerous organizations devoted to scientific excellence and is a member of Phi Beta Kappa sind Alpha Omega Alpha

honorary societies. At the present time, he is Associate Professor of

Medicine and Instructor in Physiology, Tufts University Medical School;
xix Assistant in Medicine, Harvard University Medical School; Chief of

' Gastroenterology and Director of the Metabolic and Gastrointestinal

Research Laboratories at the Lemuel Shattuck Hospital.

Raja N. Khuri was born in Beirut, Lebanon and received both his B.Sc. degree (1955) and M.D. (1959) from the American University of Beirut.

The following year he was a Junior Assistant Resident in Medicine at the

American University Hospital (Beirut) and, from 1960 to January 1964, was a Postdoctoral Research Fellow at the Harvard Medical School. He

returned to the American University of Beirut as Assistant Professor in Physiology and Internal Medicine (1964-68) and became Associate

Professor and Chairman of the Department of Physiology in 1968. During 1968-69, Dr. Khuri has been Visiting Associate Professor of

Physiology at the Yale University School of Medicine.

His research interests are concerned with ion-selective microelectrodes

and their applications to biological systems, in general, and to studies in renal physiology, in particular.
XX ION-SELECTIVE ELECTRODES

Garry A. Rechnitz received his undergraduate and graduate education

at the Universities of Michigan and Illinois, respectively, spent five years on the faculty of the University of Pennsylvania, and is now Professor of

Chemistry and Associate Provost for Natural Sciences and Mathematics

at the State University of New York at Buffalo. His research interests in- clude the properties and applications of ion-selective membrane elec- trodes, controlled-potential coulometry, the kinetics and mechanisms of

analytical reactions, and other aspects of modern analytical chemistry.

He is the author of more than sixty publications (including two books) in these areas. Dr. Rechnitz is a member of the editorial advisory boards for Talanta

and Analytical Letters as well as of a number of technical and honorary

societies. Since 1966, he has been a fellow of the Alfred P. Sloan

Foundation.

Truman S. Light was born in Hartford, Connecticut, received a Bachelor's degree in Chemistry and Physics from Harvard College,

a Master's degree in Analytical Chemistry from the University of

Minnesota and a Doctorate in Inorganic Chemistry from the University
xxi

of Rome. From 1949 to 1959, Dr. Light was an Instructor and Assistant

Professor at Boston College teaching Analytical Chemistry with emphasis on Physical Chemical Methods of Analysis. From 1959 to 1964, he was employed by the Avco Corporation. Research and Advanced

Development Division in Wilmington, Mass.. as a staff Scientist working on high temperature materials for the space industry and their related

analytical problems. Since 1964, Dr. Light has been with The Foxboro

Company. His research interests and publications are in the fields of

analytical chemistry and application of instrumental methods of analysis

to process control. His current research is concerned with studies of

ion-selective electrodes. Dr. Light is a member of Sigma Xi, the American Chemical Society,

the Instrument Society of America, the Society of Applied Spectroscopy

and the New England Association of Chemistry Teachers.

Richard A. Durst is a research chemist and project leader in elec- troanalytical measurements in the Microchemical Analysis Section of the

NBS Division of Analytical Chemistry. He was graduated with Highest

Honors from the University of Rhode Island (B.S. — 1960) and received

his Ph.D. in analytical chemistry from the Massachusetts Institute of

Technology (1963). While at M.I.T., he was a NSF Fellow and con- ducted polarographic research and electrolyte solution studies under the

direction of Prof. D. N. Hume. Dr. Durst was aNRC-NBS Postdoctoral

Research Associate with Dr. J. K. Taylor (1963-64), Visiting Assistant

Professor at Pomona College (Calif.), Assistant Professor at Boston College ( 1 965-66), and returned to NBS in 1 966.

His general research interests include instrumental methods of analysis

with emphasis on electroanalytical techniques. Presently, he is studying

the analytical applications of ion-selective electrodes, especially for microanalysis.
xxii ION-SELECTIVE ELECTRODES

Dr. Durst is a member of the American Chemical Society, the A. A.A.S.. Sigma Xi, Phi Kappa Phi, the Polarographic Society (London),

the Chemical Society of Washington, and a Fellow of the Washington

Academy of Sciences.
CHAPTER 1 THEORY OF MEMBRANE ELECTRODE

POTENTIALS: AN EXAMINATION OF THE

PARAMETERS DETERMINING THE

SELECTIVITY OF SOLID AND LIQUID ION

EXCHANGERS AND OF NEUTRAL

ION-SEQUESTERING MOLECULES

George Eisenman

Department ofPhysiology

University of California Los Angeles, California

I. Introduction

Membrane electrodes specific to a wide variety of ions are coming of

age, as evidenced by the contents of this volume. From the discovery by

Cremer [1] and Haber and Klemensiewicz [2] at the beginning of the

century of the H+ selective glass electrode and the development in the

late fifties by Eisenman and his colleagues [3-6] of specialized glass compositions specifically selective to ions such as Na+, K+, Ag+, NHJ , T1+,

Li+, and Cs+, we have recently progressed to the use of liquid ion exchangers for divalent cations [7] and a variety of anions [8] . Electrodes based on solid-state crystals have been developed by Frant and Ross [9], and

a new variety of specific ion electrodes is just emerging, based upon the

specific sequestration of cations by neutral macrocyclic molecules (typically cyclic antibiotics and polyethers) which offer the possibility of

exquisite selectivity, entirely comparable to the very high selectivities characteristic of biological mernbranes [10-12]. The mechanism by

which these uncharged molecules produce such highly specific electrodes

o in ultra-thin (100 A ) phospholipid bilayer mernbranes has been shown

recently to be due to the action of these molecules as specific solubilizers

of cations within the liquid-like interior of these membranes [ 1 3 , 1 4] . Bulk

solvents containing such materials have also been reported to produce

highly specific responses for ions such as K+ and Rb+ [12], but with

sub-ideal slopes. The above types of membranes can be conveniently

categorized into three general types which share a number of common

features but have important theoretical and practical differences: (A)

solid ion exchangers, (B) liquid ion exchangers, and (C) neutral sequestering agents.

I will begin by summarizing the principle theoretical expectations from

the analysis of the origin of the membrane potential for each of these three

1
2 ION-SELECTIVE ELECTRODES

types of electrodes, referring the reader to appendices for details, but explicitly examining in the test the parameters determining the ionic selectivity in each. The similarities and differences between these mechanisms

as well as their particular advantages and limitations will then be

discussed. Only monovalent cations will be considered, as a parallel line of argument applies in the case of monovalent anions.

II. Solid Ion Exchangers (e.g., The Glass Electrode)

When a thin membrane of glass is interposed between two solutions, an

electric potential difference is observed which depends on the ions

present in the solution in a simple and reproducible manner [3-6]. Depending on the composition of the glass, the response may be to H+

chiefly [2] or it may be to other cations such as the alkali metal cations

[3], the alkaline earths cations [5], or even certain organic cations [5]. The experimental evidence is now overwhelming that such glass elec- trodes are simply cation exchange membranes having a particularly high

degree of selectivity among the various monovalent cations [ 15]

.

The theory of the origin of the membrane potential of such electrodes

begins with the solution of the flux equations for liquid junctions by

Planck [16] and Nernst [17]. This was first applied to semipermeable

membranes by Teorell [18,19] and by Meyer and Sievers [ 20] by including the effects of Donnan equilibria at the membrane-solution interfaces. Helfferich [21] and Mackay and Meares [22] extended the analysis to include boundary conditions appropriate to ion exchangers. Karreman

and Eisenman [23] postulated that glass electrodes were simple cation

exchange membranes characterized by "n-type" non-ideal behavior (for

which the derivative of the logarithm of the activity with respect to the

derivative of the logarithm of the concentration is a constant) and obtained analytical expressions for the glass electrode potential in terms of

the ion exchange equilibrium constants and mobilities of the cation species characteristic of the glass. This work was extended and generalized

by Conti and Eisenman [24,25] with the results summarized in Appendix

Section A. Nicolsky and his colleagues [26], as well as Doremus [27]

and Isard [28] have recently carried out a theoretical treatment in agree- ment with these; and the theory is now generally accepted [6]

.

Glass electrodes are made from mixtures of oxides of elements of oxidation state 3 or greater {e.g., Si, Al) with oxides of elements of oxidation

state 1 or 2 {e.g., Na, Ca). When melted and subsequently cooled, such

oxides form a three-dimensional solid in which the most mobile charged

species are the monovalent cations. A membrane made of glass is there- fore permeable almost solely to cations and functions as a cation

exchanger with the consequence that a Nernst potential is observed when

such a membrane separates two solutions of a single salt at two different
THEORY OF MEMBRANE POTENTIALS 3 concentrations:

(1)

where a,' and a" represent the activities of the cation 1+ in the two

aqueous solutions designated by (') and ("), on either side of the membrane. R is the gas constant, T is the absolute temperature, and F is the

faraday constant.

If an electrode is constructed by filling a thin walled glass bulb with a

solution of a salt of constant composition, the electric potential measured

using such a half cell depends only on the activity of 1+ in the external

solution (') and can be written simply as:

This provides a means of measuring the activity of cation 1+ in different

solutions provided only that an appropriate reference electrode is used to complete the electric circuit. If a number of species of cations are present simultaneously, the

theoretical analysis of Appendix Section A as well as experimental stu- dies on certain hydrated glass compositions [15] as well as dry glass [29]

inform us that the membrane potential depends on the weighted contributions of each ionic species according to the equation:

For simplicity, I have restricted considerations to two species of cations,

1+ and J+, and also considered only the case in which ideal behavior exists

{i.e., n = I). Equation (3) is time independent, applying at all times subsequent to the establishment of equilibria at the membrane-solution inter- faces [24].

The parameter [{ufluf)Kij] in Equation (3) is a weighting factor

characteristic of the selectivity of a given membrane composition. A

value of [(u*/uf )A:ij] = 10 implies that ion J+ is 10 times as effective on a mole for mole basis as ion 1+ in determining the electrode potential.

The selectivity between 1+ and J+ is determined by the product of the mobility ratio of these species in the membrane (u*/uf) and the ion ex- change equilibrium constant (Kij) characteristic of their exchange

between the aqueous phase and the membrane:

J+ (aqueous) + /+*(membrane) (membrane) + /+ (aqueous). (4)

E= Const + —F

In Gj , (2)

(3)
4 ION-SELECTIVE ELECTRODES

[In Eqs. (3-4). and henceforth, asterisks are used to denote quantities

characteristic of the membrane phase; while quantities relating to the

aqueous phase will either be unmarked or will be designated by (') and (")

when it is necessary to distinguish between the solutions on two sides of

the membrane.]

III. Liquid Ion Exchangers

Membranes composed of a water-immiscible solvent interposed

between two aqueous solutions were among the first membranes whose

electric properties were characterized [30]; their history has recently

been summarized by Shean and Sollner [31]. When such membranes

contain an appreciable concentration of an ionizable species which is preferentially soluble within the membrane phase {e.g., a fatty acid or an

aliphatic amine), they function as liquid ion exchangers [32] , which differ from solid ion exchangers in that the ion exchange sites are free to move

within the membrane. The situation in such a membrane is diagrammed

in Figure 1 , where the arrows indicate that the cation species, I+, is freely

permeable across the membrane-solution interfaces whereas the organophilic anion, S~, is "trapped" within the membrane phase. As a con- sequence of this, the aqueous anion species, X~, is excluded from the

membrane phase.

SOLUTION(') solutionCO

I*"

Figure L Diagram of a liquid ion exchanger membrane (reproduced from Fig. 1 of [34]).

I^, S". and X~ refer to the counterions, the site, and the co-ion species, respectively. Asterisks for the species in the membrane have been omitted for simplicity.
THEORY OF MEMBRANE POTENTIALS 5 A. Limiting Case of Complete Dissociation

Conti and Eisenman [33] have shown that, in the limiting case of

negligible association, the membrane potential is given by:

E='^\n — '(5)

Equation (5) is valid both in the steady state and also instantaneously subsequent to a step change in solution conditions [34] and can be seen to be

identical in form to Equation (3) characteristic of solid ion exchangers;

here uf is the mobility of the dissociated 1+ species in the solvent phase

and ki is the partition coefficient of 1+ between water and the solvent of

the membrane:

(aqueous) ^

' ^ /+* (membrane) (6)

Equation (5) indicates that the selectivity between species 1+ and J+ is determined by the partition coefficients and mobilities of the dissociated

ions. The selectivity is therefore determined entirely by the solvent and is independent of the particular organophilic exchanger, which is not sur- prising since dissociation between the liquid ion exchanger molecules and

their counterions is complete.

B. Limiting Case of Strong Association

Because of the low dielectric constant of the solvents typically used for

liquid ion exchange membranes, association of the species I + * and

S~* is expected within the membrane phase according to reaction:

+ /S* (7) which results in the formation of the neutral pairs IS , which are freely

mobile within the membrane. K;^ is the association constant for the for- mation of neutral pairs within the membrane phase.

For such a system, Sandblom, Eisenman, and Walker [34] have shown

that the electrode potential is given by:

a'i-\- (1-t) In ^

' /'^ +Tln

a"i +

I -) (8)

both "instantaneously" and in the steady-state (see Appendix Section B).
6 ION-SELECTIVE ELECTRODES

The electrode potential of a liquid ion exchanger membrane in which

strong association occurs is seen to consist of two logarithmic terms, each

of the form of the previous electrode equations. The relative contributions

of these terms are governed by the parameter:

T= ^— — ^ — 0 ^ T ^ 1 (Q^ {ur+uf)uf,K%-{uf+ut)ur,Krs '

The selectivity in the first term of Equation (8) depends on the product of

the partition coefficient ratio of the dissociated ion species {kjlki) and the

ratio of the summed mobilities of the dissociated ions and the dissociated

sites [(u* + u/)/(u* + Us*)] . It therefore depends predominantly on

the solvent and only depends on the chemical nature of the liquid ex- changer through its effect on Us*. On the other hand, the selectivity in the second term of Equation (8) is determined by the product of the

mobility ratio of the neutral pairs (ufjufg) and the ion exchange equilibrium constant (Kij) of the reaction:

K i

'

y+ (aqueous) (membrane) JX^ (membrane) +/+ (aqueous),

(10)

which is formally identical to the reaction shown as Equation (4). Kij can

alternatively be expressed as the product of the partition coefficient ratio of the ions and the association constants in the membrane phase as:

The selectivity of Kij depends on the properties not only of the organophilic ion exchanger molecule but also on the solvent in which it is dis- solved, as will be examined in Section V. The value of r, which lies between 0 and 1 , depending on the properties of the solvent and of the ion

exchanger, determines the relative importance of the two logarithmic

terms of Equation (8). For certain systems. Equation (8) is largely determined by either the

first or the last term, depending on whether r is zero or one. For example,

if the association constant for the 1+ species is much larger than that for

J+, and if the mobilities of all neutral pairs are approximately equal so

that u* = Ujl , Equation (9), reduces to:

uf + at (12)

from which (1 - r) is seen to be simply the transference number of the

most dissociated counterion species and r is identifiable as the trans-
THEORY OF MEMBRANE POTENTIALS 7

ference number of the dissociated site species relative to the most dis- sociated counterion species. This means that, if the dissociated site species is more mobile than the most dissociated counterion, the second term

will determine the potential predominantly, as appears to be the case ex- perimentally for H+ and Na+ with the exchanger bis-2-ethylhexyl

phosphoric acid in amyl alcohol [32]. The similarities and differences

between solid and liquid exchangers are given by comparison of Equations (3), (5), and (8).

IV. Neutral Sequestering Agents Which Act as Molecular Carriers of Ions

In 1964, Moore and Pressman [35] discovered that neutral macrocyclic antibiotics induced ion permeation in mitochondria, and comparable electrical effects of these compounds on artificial phospholipid bilayer

membranes were demonstrated shortly thereafter by Lev and Buzhinsky

[10] and by Mueller and Rudin [11]. Bulk solvent electrodes based on

these molecules were developed by Stefanac and Simon [12]. More

recently, the related, but structurally simpler cyclic polyethers synthesized by Pedersen [36] have been found to produce cation-selective membrane electrodes with selectivities entirely comparable to those characteristic of the antibiotics [13,14]. These molecules are devoid of charged

groups but contain an arrangement of ring oxygens energetically suitable

(through ion-dipole interaction) to replace the hydration shell around cat- ions. These lipid-soluble molecules are thus able to solubilize cations in organic solvents, forming mobile charged complexes with the cations

therein, and in this way providing a mechanism for cation permeation

across such (normally insulating) media. Chemical formulas and

space-filling models of two such molecular carriers of cations are illus- trated in Figure 2. The membrane system corresponding to this mechanism is diagrammed

in Figure 3 and resembles liquid ion exchangers in its fluid nature. It dif- fers from these, however, in that the complexed cation species (IS+) bears

the charge of the sequestered cation instead of being electrically neutral. As a consequence of this, the most interesting properties of such carriers

in low dielectric constant solvents are manifested in ultra-thin (60A)

membranes [37] in which a sufficient excess of cations is brought into the

membrane in the form of the sequestered species to lead to a substantial deviation from electroneutrality [38]. (Indeed, the excess of

complexed-cations solubilized in the membrane is sufficient for the concentration of free cations and anions to be regarded as negligible in the

membrane [38].) In solvents of higher dielectric constant these molecules

produce useful electrodes of much greater thickness [12], but since the

published data on such systems are scanty in comparison to that for the
8 ION-SELECTIVE ELECTRODES

thin membranes, I will confine my comments to the latter case, noting that

its essential features should bear on the thicker systems as well. A. Membrane Potential

A theory for neutral carriers has been developed by Ciani, Eisenman,

and Szabo for dilute aqueous solutions in which the concentrations of the

neutral macrocyclic molecules are identical on both sides of the membrane [13,14,38]; and the membrane potential [i.e., the potential dif- ference between solutions (") and (')] at zero current in mixtures of two

0% CHj CH3 P CH3

' °v

0 CH3 I I CH3 MONACTIN

a X)

DICYCLOHEXYL-18-CROWN-6

Figure 2. Chemical formulas and space-filling models of the molecular carriers of ions, dicyclohexyl-18-crown-6 [36] and Monactin. (Reproduced from Fig. 1 of [13].) A sphere

approximating the size of K+ has been inserted in the ring of the CPK model of dicyclohexyl-18-crown-6 (abbreviated as XXXI). The monactin molecule is shown in an arbi- trary open configuration. While neither of the molecules has a net charge, they both can, through their ring oxygens, provide an energetic environment for cations similar to that

in water. Since the nonpolar exterior of the rings causes the molecules themselves to partition favorably into hydrocarbon solvents, they are expected to solubilize cations in low dielectric media. Note that while monactin is a flexible molecule capable of under- going considerable configurational changes on interaction with cations, XXXI is more

rigid and not susceptible to much deformation from a planar configuration.
THEORY OF MEMBRANE POTENTIALS 9

cations 1+ and J+ has been shown to be described by:

£= —In i4Kj

(13)

where KjKi is the ratio of the equilibrium constants of the salt extraction

reactions

Ki

(14)

(15)

which measure the extent to which the neutral molecules, S , can extract

the salt, I+X", from water into an organic solvent phase [14].

0 d

SOLUTION (0 MEMBRANE SOLUTION ('0

Figure 3. Diagram of a neutral-carrier membrane (reproduced from Fig. 2 of [13]). I+, S, IS^, X~, and ISX refer to the free ion, the neutral molecular carrier, the complexed

cations, the free anion and the neutral complex, respectively. Asterisks for the membrane

species have been omitted for simplicity.
10 ION-SELECTIVE ELECTRODES

Note that KjlK-, is formally identical to Kij, the equilibrium constant of

the reaction:

KJ+ (aqueous) +/>S^ *( membrane) ^=z^ (membrane) +/+ (aqueous).

(16)

Although Equation (13) is identical in form to Equation (3), characteristic of solid ion exchange membranes, it must be emphasized that the

physical meaning of the selectivity parameters is quite different. In many

practical instances the size and charge of the complexed-cation appears

to be virtually independent of the particular cation sequestered [39,40]

so that the ratio (Uj^/u/*)=l. In these cases we have the very simple

result that the electrode selectivity depends solely on the ratio, KjlKi, of

equilibrium constants.

V. The Factors Determining Selectivity for Each of These Types of

Membranes

The factors determining the relative ion selectivities for these various

types of electrodes can be compared most easily with the aid of Table 1

,

which summarizes the selectivity parameters from Equations (3), (5), (8), and (13) for solid ion exchangers, dissociated liquid ion exchangers, as- sociated liquid ion exchangers, and neutral carriers, respectively. From

the column labelled "Exact Representation" it should be clear that mobility, as well as equilibrium factors, determine the electrode potential

selectivity for each of these mechanisms. However, from the column

labelled "Approximate Representation" it can be seen that mobility terms

contribute only slightly to the selectivity of certain liquid ion exchange

membranes, and not at all to neutral carrier membranes. The physical reasons for this will become more clear from examining each of these

mechanisms in greater detail now; while the factors underlying the

equilibrium ion exchange selectivity of these electrodes will be considered in Section VI.

A. Solid Ion Exchangers

Scrutiny of Equation (3) indicates that the relative effects of species 1 +

vs. on the electrode potential of a given membrane depend on the rela- tive mobilities of these species in the membrane {u^luf") as well as on their ion exchange equilibrium constant {Kij). It is expected, and observed [ 1 5,25] , that the more strongly an ion is preferred by such an ion

exchanger, the more poorly does it move within the membrane; since the more difficult it is for it to jump from site to site. For this reason, there are opposing effects between mobilities and affinities of ions in solid ion
THEORY OF MEMBRANE POTENTIALS 11

Table 1. Selectivity parameters for the various types of membranes.

Exact Approximate

representation representation Comments

Solid ion exchangers K;

U.4 mobility opposes

K-- equilibrium

selectivity

Liquid ion exchangers

Dissociated u.^ k.^

u^+ L +

u and k depend

only on solvent,

are independent

of exchanger

species

Associated

( T = 0 , poorly

mobile sites)

U.++U -\k.+

U.++U -/k.+

1 S / 1

( T = 1 , highly

mobile sites)

u.

u.

'is

Neutral carriers K. K. K K.

exchangers, which constitute one of the principle Hmitations of such

systems.

For example, the ten-fold electrode potential selectivity for K+ over Na+ of a typical K+-selective glass electrode is the result of a nearly hundred-fold ion exchange preference of the glass for K+ over Na+ opposed

by a nearly ten-fold lower mobility of than Na+ [41]. The relatively

low selectivities of such solid ion exchangers for divalent cations appears

to be a consequence of the poor mobility of these species [4 1 ,42]

.

Part of this limitation is overcome when one allows the ion exchange

sites to move by making the ion exchanger a liquid in which the (neutral)

complex between the counterion and the mobile-site can move; but an

THEORY OF MEMBRANE POTENTIALS 13

8 §

i

° ^ c

•o .2 C -o

<U ID

"2 «= § 2

5 s

'-5 o

1)

C lU

(U X) E ^

<L) O

S" ^(L) <U ^

.£ E o ^ t ^ ^ o

O _4)

Of) OJ U, C

E

- o a

•o _

o o

O cd ^ ^!

E

3 O _C3 —

.2 £= *- cd O S (U c

OX) .E >

c/) > I

3

O c« o I I

cd > ^1

o .Si

60 cd 3

(U ^

C/5 O

1- T3

(U CJ

(/) c3

CJ (U ,CJ

c E

03 O

Ob =

oa E

(J c S I

O <u

<u c

E o

c >^ 11o

2>

qj C

E a> S 3

CJ CJ Is T3

• E "O £ 'Si

o

C/5 O J£

a, c3 it

^ d

w (U

c« > 3

o- o

<L) (Ua.

E o — 1)

ofi 5

(U "O

OJD ^

C O

cd "~r a D.

-5

ofl Z

O O

9 >

3 >
14 ION-SELECTIVE ELECTRODES

16 ION-SELECTIVE ELECTRODES

even greater improvement will be seen to occur for the neutral carrier

mechanism, in which the complex between the counterion and neutral

carrier molecule is electrically charged. Despite this limitation, solid ion

exchangers offer a variety of electrodes suitable for measuring

monovalent cations such as H+, Li+, Na+, K+, Rb+, Cs+, Ag+, T1+, NH^

,

and even certain substituted ammonium, amines, and amino acids [3 ,5,6]

.

Typical data illustrating the kinds of selectivity characteristic of these

electrodes are presented in Figures 4 and 5. The selectivity among ions is a function of the ion exchanger composition, as can be seen by the dif- ferent magnitudes and sequences of selectivity observable in the various

glass compositions of these figures, where the Roman numerals indicate

the selectivity sequence (defined on page 30) characteristic of the elec- trodes under the indicated conditions.

At present, glass electrodes are the electrodes of choice for H+, Na+,

Ag+, and Li+, for which their specificity is sufficiently high and their excellent stability characteristics are desirable. In addition, since these elec- trodes function well in organic solvents [6] they can be used in non-aque- ous media, as well as in the presence of lipid-soluble or surface-active

molecules [6,43].

B. Liquid Ion Exchangers

Examination of Equation (5) and Table 1 indicates that for a strongly

dissociated liquid ion exchanger (such as might be expected in solvents of

sufficiently high dielectric constant) the selectivity among various ions

should be completely independent of the chemical properties of the lipophilic ion exchanger molecule other than the sign of its charge. Thus,

nitrobenzene or nitromethane can be caused to become a cation-selective

electrode by adding oleic acid to them [32]. Such a membrane exhibits

high specificities among cations, as illustrated by the data of Figure 6. The

effect of oleic acid also occurs with long chain sulfonic or phosphoric

acids; and the selectivities are the same [32] . It is therefore essentially in- dependent of whether the ion exchanger is a carboxylate, phosphate, or

sulfate, as would be expected from Equation (5). On the other hand, if a

lipophilic anion exchanger molecule such as dodecylamine is used instead

of oleic acid, the nitrobenzene membrane becomes an anion-selective

electrode highly selective for I" > Br- > CI" > F" [44]. For a liquid ion exchanger in which association between counterion and

site cannot be neglected (as for a solvent of low dielectric constant), the

origin of selectivity is more complex and generally is a function of both

the solvent and the exchanger since, even for the limiting case of strong

association, separate contributions of the solvent and exchanger can be

seen in the two terms of Equation (8). In the first term, which dominates the properties of the system when

T=0 (as for example with sites which are poorly mobile compared to the
THEORY OF MEMBRANE POTENTIALS 17 + 100

mV

-200

—log Ccat

Figure 6. Cationic selectivity of liquid ion exchanger electrodes based on the solvent nitrobenzene. (Reproduced from Fig. 6 of [32].) The membrane is nitrobenzene containing

5% oleic acid. The points indicate the observed potentials at neutral pH. Note the large

selectivity differences among the alkali cations. These are essentially independent of whether the added exchanger is a carboxylic, sulfonic, or phosphoric acid. Interestingly, the solid curves are drawn according to Equation (1) but the deviation from the Nernst

behavior at the lowest cation concentrations is presumably the result of the dissolving of

the sites rather than due to the effects of other cations because, at neutral pH, the H + effect is far too small to account for this deviation.
18 ION-SELECTIVE ELECTRODES

counterions), only the properties of the solvent appear in the "Approximate Representation" of Table 1. Since the mobility of the site species can be neglected in comparison to that of the counterions in this case, the parameters determining the selectivity become essentially the same

as those for the completely dissociated case, namely u^/u^ and kj/ki, both of which are independent of the chemical nature of the lipophilic

exchanger since they represent properties of the dissociated ions alone. The selectivity of the second term of Equation (8), on the other hand,

which can dominate the properties of the membrane when t= 1 (as for ex- ample with sites which are highly mobile compared to the counterions),

depends not only on the properties of the solvent but also on the chemical

properties of the sites, since these affect both the ion exchange equilibrium constant {Kij) and the mobility ratios (uj|/uj) of the neutral

complexes between the counterions and the sites. (For the usual ion

exchangers like dodecylphosphoric acid, these mobilities should depend to some extent on the counterion, although for cyclic molecules like monensin [45] which can sequester cations in a manner similar to the

neutral carriers discussed below [46] , this ratio could approach unity.)

It will be instructive to examine the values of these parameters for a

typical liquid ion exchange system consisting of bis-2-ethylhexyl

phosphoric acid (abbreviated hereafter as "HBis") dissolved in n-amyl al- cohol, for which these have been measured experimentally for H+ and

Na+ [32]. The values of the association constant, single ion conductances, and distribution coefficients (S°) are presented in Table 2,

together with the value calculated for these [32] for the ion exchange

equilibrium constant /^HNa- These parameters should suffice in Equation

(8) to deduce the selectivity to be expected for the electrode potential.

Since r is nearly unity. Equation (8) can be approximated by its second

term alone, namely:

f

I ^HBis Y r,' ^ .

I u*,^s r " ^ ''a;; + o.oooo5a:;.«' ^^'^

provided u^gis^ u^aBis- From Equation (17) and the data of Table 2, this membrane system is expected to be highly selective for H+ to Na+, which is in agreement with

the experimental observations in Figure 7, where a large H+ to Na+ selectivity is seen. Thus, the selectivity characteristic of the equilibrium ion

exchange appears to account for the principle selectivity observable as a membrane electrode.

Note that the selectivity of the ion exchange equilibrium constant Kij of

Equation (10) is not solely a property of the ion exchanger molecule but
THEORY OF MEMBRANE POTENTIALS 19

Table 2. Association constants, single ion conductances, distribution

coefficients, and the calculated ion exchange equilibrium constant for bis—2—ethyl hexyl phosphoric acid in wet n—amyl

alcohol.®

HBis

NaBis

4.4 X 10^ cm^ mol

1.8 X 10^ cm^ moF^

1.47 ohm~^ cm~^ mol

^

18.56 ohm" ^ cm" ^ mol

^

9.99 ohm~^ cm"^ mof ^

Bis

0.88

^Ci

^aCl

0.022

0.0025

KHNa

CO'^NaCl

~|2

'HCl

KNaBis

0.00005

KHBis

^^HBis ^NaBis association constants of Eq. (7) in wet n—amyl alcohol; A° ^, A°, A° are the single ion conductances;

S^Q^ and SgfgQj are the limiting partition coefficients of HCl and

NaCl between and wet n— amyl alcohol. For further details, see reference [32] . depends also on the solvent of which the membrane is made. This can be

seen by writing Kij explicitly in terms of standard chemical potentials:

RT \n Kij = iJL°j. (membrane) — /i,J,, (membrane) + />t°+ (aqueous) — (aqueous). (18)

Since ptj+ (aqueous) and /lc-+ (aqueous) depend only on the aqueous
20 ION-SELECTIVE ELECTRODES

-2.0 0 2.0 4.0

-log a cat

Figure 7. Electrode response to the indicated alkali metal cations of wet n-amyl alcohol containing 10% bis-2-ethylhexyl phosphoric acid. (Reproduced from Fig. 5 of [32].) The reference solution on one side of the membrane was 0.001 N HCl in all cases: while

that on the other side had the concentrations of the chlorides indicated for each cation on the abscissa.

phase, the only terms depending on the membrane are jxl^ (membrane)

and fjL°j, (membrane). As the energy of taking the pairs IX and JX from

a convenient reference state {e.g., in a dilute gas) into the membrane de- pends on the dielectric constant of the solvent and the electric field of the

ion-site dipole, which is a function of the ion exchanger molecule, [/u-^.
THEORY OF MEMBRANE POTENTIALS 21

(membrane)— (membrane)] depends on both the properties of the

solvent and of the exchanger.

C. Neutral Carriers

Equation (13) and Table 1 present the extremely simple selectivity ex- pectations for the neutral carrier mechanism typified by a variety of neutral macrocyclic molecules [14]. For these molecules, I have pointed out above that it is reasonable to expect that the mobilities of the complexed

cations are the same for all cations, for which situation selectivity is deter- mined solely by equilibrium parameters, as indicated in the "Approximate

Representation" of Table 1, where only the ratio KjlKi appears. The

neutral carrier mechanism differs from that of the ion exchangers in that charged ion exchange sites are not present. Instead, the "sites" are

neutral molecules which form stoichiometric complexes with cations and

function as carriers for these, the complex being charged.

Typical data for such a membrane are presented in Figure 8 which

demonstrates the electrode potentials characteristic of the antibiotics

nonactin and trinactin in mixtures of K+ with Li+, Na+, Rb+, and Cs+

[14]. The points represent experimental observations; while the curves have been drawn according to Equation (13) with the values for the selectivity parameters labelled on the figures, designated as PilPk'. PilP, = {uSKi)l{utJCK) (19)

The agreement of the data with Equation (13) is seen to be excellent; and

the selectivity among the cations is very high (note that the K+ to Na+

selectivity of nonactin is better than 130 to 1). The sequence of selectivity

among the group la cations for both nonactin and trinactin is K > Rb >

Cs > Na > Li (which is selectivity order IV to be defined below), but it is clear that systematic quantitative changes in selectivity occur as a function of increased methylation of the antibiotic (trinactin has 3 more

methyl groups than nonactin). The significance of these will be com- mented on further in the following section.

Entirely comparable data are also characteristic of Pedersen's cyclic

polyether, dicyclohexyl-18-crown-6 [36], as is illustrated in Figure 9, although it should be noted that the electrode slope is slightly sub-Nernstian, being only 50 mV in this case. Nevertheless, the selectivity of

to Na+ is again very high, being 1 25 to 1 for this molecule [13].

High selectivifies of neutral carriers have been reported for considerably thicker membrane systems, such as monactin in CCU [12],

valinomycin in hexane [47], and valinomycin in octanol [48]. Tosteson

has also found high K+ over Na+ selectivities for valinomycin, a mixture

of monactin-dinactin, as well as for a cyclic polyether using thick
22 ION-SELECTIVE ELECTRODES

Figure 8. Membrane potentials of lecithin bilayers in the presence of Nonactin and

Trinactin. (Reproduced from Fig. 8 of [14].) The points represent the experimentally observed values of potential; while the curves are drawn according to Equation (13) with the indicated values of Pil P^, = (Ui^ Ki)l(Uk* Kk).
THEORY OF MEMBRANE POTENTIALS 23

0 MCI

Figure 9. Membrane potentials in alkali chloride-potassium nitrate mixtures containing

10"^ molar Pedersen's cyclic polyether XXXI [36], labelled here D206 in the terminology

of [13]. (Reproduced from Fig. 4 of [13].) The membrane was formed in an aqueous \Q--M solution of the indicated alkali chloride containing IQ-^M XXXI. The points are experimental; while the curves have been drawn according to the equation indicated on

the figure. lipid-containing membranes [49] . Clearly the mixture need not be as thin as the bilayers of Figures 8 and 9. Because of the relative newness of this system, I will describe its chemistry and properties in somewhat greater detail than was done for the more familiar ion exchangers examined above. Recall Figure 3, in which

o the membrane is represented by a thin {e.g., 60 A ) liquid hydrocarbon

phase interposed between two aqueous solutions, designated by (') and

("). The neutral macrocyclic molecules (such as those illustrated in Fig.

2) are assumed to be preferentially partitioned in the organic phase and to form stoichiometric complexes with cations, thereby solubilizing them in the membrane.^

If the membrane phase is of low dielectric constant, then the concentration of dissociated ions in it will be low (witness the high electric re- 'The membrane need not be thin, although 1 will restrict myself to this situation here since

it is only for this case that a rigorous membrane theory has been derived and tested

[ 1 3,38] . Indeed, in order to characterize the equilibrium properties for comparison

with the electrical properties of bilayers. the membrane phase has been expanded

into a bulk liquid and the salt extraction properties of the macrocyclic molecules

characterized.
24 ION-SELECTIVE ELECTRODES

sistance of artificial bilayer membranes in the absence of added materials

[37] and the low salt uptake characteristic of pure hydrocarbon solvents

[39]). However, in the presence of lipid-soluble neutral macrocyclic

molecules, both the electric conductance of thin membranes and the salt uptake by bulk phases are increased markedly [13] because of the ability

of such molecules to solubilize the cations by providing an energetic en- vironment for these comparable to that in water. Three independent types of species exist in the aqueous as well as in the organic phases: the free cations (I+), the free anions (X^) and the free neutral macrocyclic molecules (S). For n species of monovalent cations, n reactions of the type

/+ + S^=^/S+, (20) Kts occur between the cations 1+ and the macrocyclic compound S, leading to the formation of the positively charged lipid-soluble complexes IS+, as in- dicated by the equilibrium between the upper three species in Figure 3. Also indicated in Figure 3 is the possibility of further association

between the IS+ species and the anions X" according to the reaction:

IS^+X-^=^ISX ; (21)

which is usually negligible in its effects on the electrical properties of the

membrane [ 14]

.

When an aqueous solution is in contact either with a bulk organic sol- vent or with the membrane, viewed simply as a thin membrane-like portion of the solvent, the equilibrium distribution for each species between

the two phases can be described by heterogeneous reactions of the type:

5*, k.= aflas, (22)

for the neutral species (S and ISX) and of the type:

ai exp

ki „ „

\ziF\\f

RT ai exp - (23)

for the charged species (/ = I + , IS + , X") where n is the oxidation number

of /. For the species /=1S + , subtracting Equation (22) from Equation (20)

and adding Equation (23) we get:

/+ + 5*^=±/S+*, (24)

ks
THEORY OF MEMBRANE POTENTIALS 25

which is a heterogeneous reaction expressing the formation of the complexed-cation species IS+* within the organic phase in terms of the

aqueous concentration of 1+ and the concentration of S* in the organic

phase. By simply adding Equation (23) for l=X- to Equation (24), we

get:

/+ + S* +Z-^=:±/5+*+Z-*, (25)

ks which expresses the extraction of the salt I+X~ from the aqueous phase

into the organic phase.

When the partition coefficients, kis, of the complexed cations are much

higher than those of all the other ions, electroneutrality does not hold in the thin membrane; and the IS+ complexes are present in excess as a "space charge" [38] . Since they then constitute the predominant charged

species in the membrane, its electrical properties can be described solely

in terms of the parameters appearing in the equilibrium constant of Equation (24): K; = -^'

(26)

This constant can normally not be measured directly since its determination requires a knowledge of the (unmeasurable) electrical potential dif- ference between the two phases.

On the other hand, when studying partition equilibria in bulk phases

where the electroneutrality condition governs all chemically detectable

concentrations, the equilibrium constant of reaction, Equation (25)

kisKj^kx = —7— (27)

is directly measurable. This constant differs from K,' only in its dependence on kx, the partition coefficient of the anion X-; but, of course, kx

drops out when the ratios of Kf are compared for two cation species 1 + and J+ (and a common anion X"), so that a simple relationship is expected

between the constants of Equations (24) and (25).

Comparing the ratio of Equation (26) for two different cations 1+ and J+ with the corresponding ratio of Equation (27), it can be seen that Ki_ kj^Kj

K', K, kisKt' (28)

showing that the ratio of the equilibrium constants of the reaction, Equation (24), for two different cations 1+ and J+ is identical to the correspond-
26 ION-SELECTIVE ELECTRODES

ing ratio for Equation (25). This is the argument from which we have

shown elsewhere [14] that the equilibrium ratio Kj/Ki enters into the

selectivity of Equation (13) for the membrane potential. The value of this ratio is easily measurable from studies of the equilibrium salt extraction

by these molecules into organic solvents [13,14,39].

From Equation (28), it can be seen that the factors contributing to the

ratio KjiKi are the ratio of the partition coefficients of the complexed species {kjslkis) and the ratio of the formation constants of the complexes in the aqueous solutions. A further simplification is possible for those molecules for which the

complexed species are expected to have the same approximate size. In

this case, for species of the same valence type, the ratio {kjslkis) should be

approximately unity and independent of the solvent since the complexed

species are indistinguishable from each other in size and charge. For this reason the selectivity of the system depends solely on the chemical properties of the macrocyclic molecule, as these are reflected in the formation constant of the complex in the aqueous phase. It is therefore ex- pected to be totally independent of the solvent (or lipid) of which the

membrane is made! This theoretical expectation has been verified experimentally both for bulk solvent extraction equilibrium and for membrane

electrical properties [14]. We therefore can reach the important conclusion that the selectivity of the neutral carrier mechanism should be a

characteristic solely of the molecules themselves, under these conditions.

The selectivity is a measure of the extent to which the macrocyclic

molecules can sequester cations in competition with the hydration of

these cations in the aqueous phases. The physical factors underlying this competition are similar to those previously analyzed for equilibrium ion

exchange [4,50,5 1 ] but differ because the sequestering molecule does not bear a net charge, as will be outlined in the following section.

D. Summary

It is possible to summarize the above comparison of selectivity by not- ing that there is an hierarchy of increasing simplicity of the factors in- volved in the membrane selectivity. ( 1

) For solid ion exchangers, not only

is equilibrium selectivity involved but so are the mobilities of the in- dividual ion species within the exchanger. This mobility normally varies

greatly from one species to another and partially opposes any attempt to increase electrode selectivity by increasing ion exchange selectivity. (2) For liquid ion exchangers some of the mobility limitations are circumvented but at the price of a considerably more complex behavior. (3) Membranes based on neutral carriers are the simplest in that their selectivity is principally a function of equilibrium properties and, moreover.
THEORY OF MEMBRANE POTENTIALS 27

determined largely by the specificity of the interactions with the neutral

sequestering molecules. This system therefore offers the possibility of

designing a particular molecule specifically to bind a particular cation

most effectively, without undue concern for the properties of the solvent

in which one chooses to disperse it. The versatility offered by this probably will make it worth accepting the technical difficulties of working

with such systems when developing electrodes for species to which solid ion exchangers or liquid ion exchangers are not adaptable satisfactorily.

VI. The Origin of Equilibrium Specificity

From examination of Table 1 , it should be apparent that equilibrium

selectivity factors not only control the selectivity of neutral carrier membranes but also contribute importantly to the selectivity of ion exchanger

membranes. It is therefore of interest to analyze the atomic factors in- volved in the origin of equilibrium specificity. This will be done first for the case of negatively charged (monopolar) ion exchange sites, in terms of

a simple electrostatic model examined in detail elsewhere [4,50,5 1 ] . This

model will then be extended by a heretofore unpublished analysis of the

selectivity expected for neutral dipolar "sites," bearing zero net charge.

A. Free Energy and Equilibrium Specificity

The equilibrium specificity of a given phenomenon, such as an

ion-exchange reaction, is directly related to the value of the standard

free-energy change of the ion exchange of the reactions [Equations (4), (10), or (16)] through

AF°j=- RT In Kij (29)

where for neutral carriers it will be recalled that Kij of Equation (16) is equal to KjlKj.

This free energy change can be expressed as the difference between

ion-water interactions and ion-membrane interactions by

AFfj= (F?r-Fhf ) + (F*^-FfJ (30)

where (FJ*f^ — Fj'f^) represents the difference in partial molal free energies of hydration of the ions 1+ and J + , and {Ffl — Ff;) represents

the difference of their free energies in the membrane phase. The

hydration energy differences are accurately known constants for each

pair of cations; but the free energies of interaction with the membrane phase depend upon the interaction energies therein. The problem

of analyzing the origin of equilibrium specificity thus simplifies to the

348-381 0-69—

4
28 ION-SELECTIVE ELECTRODES

problem of characterizing the affinities of the various cations for an ion

exchange site or neutral carrier molecule as a function of its chemical

composition.

The rigorous calculation of the energies of cation interaction with

molecular anionic groups for a solid ion exchanger such as glass, or for a

liquid ion exchanger molecule dissolved in a given solvent, has not yet

been accomplished; although an approximate calculation for silicate and

aluminosilicate models has successfully accounted for their selectivity

properties [4]. I will consider here only a highly simplified model in which the ion exchange site is approximated by a monopolar {e.g., halide)

model.

Consider first the simplest case in which we compare the selectivity ex- pected for the competition for a given cation between such a site and a

single water molecule as outlined diagrammatically in Figure 10 [50].

The energies of interaction of a monovalent cation 1+ of radius r+ with a

singly charged anionic site of radius r_ referred to the ions at rest in a vacuum are given by Coulomb's law as:

While its energy of interaction with the indicated tripolar model of a water

molecule is given by:

representing the net attractions between the cation and the effective

charge of the oxygen {q- = —0.64) at a distance r4 from the center of the

cation and the repulsions between the cation and the effective charge {q+ = +0.32) of the two protons at the greater distance from the center of

the cation. The energies are in kcal/mol for distances in angstroms, and

charges are expressed as fractions of the electronic charge.

Calculating the values of these energies for the various naked

(Goldschmitt) radii of the cations and inserting these in Equation (30), one obtains the selectivity isotherms, referred to Cs+. plotted on the or- dinate in Figure 10 (where AF,° is labelled AUg). This simple pro- cedure leads to a pattern of selectivity in which, for an anion site of lar- gest radius {i.e., lowest electrostatic field strength), the cations are preferred in the sequence Cs > Rb > K > Na > Li; while for an anionic

site of sufficiently small radius the sequence of preference is reversed,

being Li > Na > K > Rb > Cs. Between these extremes, the cations are

B. Ion Exchangers

(32)
THEORY OF MEMBRANE POTENTIALS 29

Figure 10. Selectivity pattern for the hypothetical cation exchange between a monopolar

anion and a single multipolar water molecule. (Reproduced from Fig. 1 of [50].) The

cation most strongly selected from water by the anionic "site" is the lowest on the chart. Above the graph are tabulated the cationic sequences (increasing specificity downwards),

defining eleven rank order designations, as a function of decreasing site radius r— Units

in kcal/mole and angstroms.
30 ION-SELECTIVE ELECTRODES

seen to pass through eleven selectivity sequences, corresponding to the

1 1 Roman numerals designating the regions between the interactions of

the selectivity isotherms of Figure 10. These sequences are:

II Rb > Cs > K > Na > Li, or Ila Cs > K > Rb > Na > Li

III Rb > K > Cs > Na > Li, or Ilia K > Cs > Rb > Na > Li

IV K >Rb>Cs>Na>Li

V K > Rb > Na > Cs > Li

VI K > Na > Rb > Cs > Li

VII Na>K > Rb >Cs > Li,or Vila K > Na > Rb > Li > Cs

VIII Na > K > Rb > Li > Cs

IX Na > K > Li > Rb > Cs

X Na >.Li > K > Rb > Cs

XI Li > Na > K > Rb > Cs

Examining the data of Figure 4, it is clear that this simple model is suffi- cient to account for the observed selectivities of glass electrodes; and it can be made more realistic by replacing the model interactions with a simple water molecule by the differences of free energies of hydration

of the cations in water, recalling that the interactions of cations with

water are constant, being given by the experimental values for (phyd_phyd) [52]^

If the sites of the exchanger are assumed in one limit to be widely

separated and the water molecules are assumed to be excluded from their

vicinity, then the free energies of interaction between cation and site (P* _p*) needed to solve Equation (30) are given in first ap- proximation by the energies as calculated by Coulomb's law in Equation

(3 1 ). The selectivity expected in this case is plotted in Figure 11 [4]

.

On the other hand, if the ion exchanger sites are assumed to be very

closely spaced (for example, with 6 sites coordinated around each cation

and 6 cations around each site), then the free energies will be given by

where the factor 1 .56 appears as a consequence of the Madelung constant

(1.75) for this coordination state and afactor of 8/9 due to the Born repulsion energy [50]. Equation (33) is the classical Born-Lande equation for the internal energy of an alkali halide crystal lattice and also depends only on r-. The expected selectivities in this case are plotted in Figure 12. Inspection of Figures 10-12 yields the following conclusions. (1) The

selectivity among cations in each of these states depends upon the radius

of the anion r_ {i.e., upon anionic field strength). (2) A particular pattern

is seen for the selectivity among group la cations in that essentially only

I Cs > Rb > K > Na > Li

(33)
THEORY OF MEMBRANE POTENTIALS 31

-3; 15.0

Q6 0.8 1.0 1.2 14 1.6 IB 2.0 2.2 A

r_

Figure 1 1 . Selectivity isotherms for widely separated monopolar ion exchange sites. (Reproduced from Fig. 16 of [4].) Negative values of free energy change of reaction (30) are plotted as a function of r- for the case of widely separated sites (see text). The Roman

numerals above the figure indicate the sequences of ionic selectivity pertaining in the regions separated by the vertical lines drawn to the intersections of the various cation isotherms. The more strongly an ion is preferred by the exchanger the lower its position on the figure.

1 1 sequences of cation effectiveness are predicted out of a possible 120. These sequences are indicated by the Roman numerals I to XI above

Figures 10-12, with only the minor variations indicated by subscript "a". The generality and usefulness of this model has recently been critically

assessed for ion exchangers by Reichenberg [53], for zeolites by Sherry

[54], and for biological membranes by Diamond and Wright [55]. In all of these diverse systems it has been remarkably successful.
32 ION-SELECTIVE ELECTRODES

40 r- %

Figure 12. Selectivity isotherms for closely spaced monopolar sites. (Reproduced from

Fig. 17 of [4].) Plotted in the same manner as Figure 1 1.

C. Neutral Sequestering Molecules

An understanding of the elementary factors underlying the specificity

of neutral molecules which bind cations can be gained from a completely

analogous analysis in which the negatively charged ion exchange site considered above is replaced by a neutral dipole, as illustrated in Figure 13. This is more appropriate as a model for the carbonyl or ether oxygens

which are the ligands in such typical neutral carrier molecules as the

macrocyclic antibiotics or the macrocyclic polyethers illustrated in Figure 2. The partial molar free energy of the complexed ion is given for the case

of such a neutral dipolar site by

, r-332 332 1

(34)

where q is the fractional value of electronic charge, N is the coordination
NEUTRAL DIPOLAR SITE

Figure 13. Models for a negatively charged ion exchange site and a neutral dipolar ligand. Described in text. number of the ligands, r+ is the (Goldschmitt) cationic radius, and r„ and

r,j are the distances from the surface of the dipole of the negative and positive charges, respectively. (This calculation lumps all repulsions between

ligands as an effective diminution of coordination number or of effective

charge.)

'I
34 ION-SELECTIVE ELECTRODES

Calculating values for these energies and inserting in Equation (30),

using Latimer's experimental values [52] for (F^^"/^— FjV^^) ,2 the selectivity isotherms of Figure 14 were deduced.

Each subfigure in Figure 14 presents a set of isotherms in the manner

of Figure 1 1. The ordinate of each subfigure is the free energy change of

Equation (30), the energy scale being given at the lower left in kcal/mole

(the lower the position of the cation, the more it is {^referred). The abscis- sa of each subfigure represents the separation (in A) of the positive pole

from the negative pole (/> - r„). This separation is zero at the right hand

side of each subfigure, in which case there is zero energy of interaction

with the dipole. Therefore, the values of energies along the right hand

edge of each subfigure are the same for a given cation on each subfigure

(corresponding simply to the differences of free energies of hydration).

The individiial isotherms are not labelled; but in all cases the horizontal

line represents the reference ion Cs+, while the sequence of isotherms at the right hand edge of each subfigure is Li+, Na+, K+, Rb+, Cs+ from top

to bottom (corresponding to the differences of free energies of hydration).

The horizontal sets of isotherms are calculated for a given (constant)

distance of the^negative pole of the dipole from the surface {i.e., "0.8" means r„ = 0.8 A); while the vertical sets of isotherms correspond to a particular product of charge times coordination number (q-N). Thus a value

iq-N) equal to 3 would correspond to dipoles of unit charge in threefold coordination or to dipoles of charge 0.5 in six-fold coordination.

The family of isotherms for the value (q-N) of 2.56 represents a particularly reasonable case of a tetrahedral coordination of oxygens having

a net negative charge of —0.64 corresponding to the Rowlinson-type

water molecule of Figure 10. These ranges of (q-N) and of r„ should en- compass all values of dipoles likely to be encountered for carbonyl or

ether oxygens in nature. This model examines what sort of specificity would be expected if the

ligand oxygens of the sequestering molecules were free to assume their distance of closest approach around each cation with negligible configurational differences of the molecule from one cation to another. Under these

circumstances, a very crude approximation of the energies of binding is given by the attractive energy of interaction between cations and dipolar

models for the ligand oxygens, neglecting differences in deformation ener- gy and entropy among cations.

Not surprisingly, when the dipole separation is sufficiently large

{I'lj-fn »f'n), the selectivities approach those calculated for the simple

-In these calculations, free energies of hydration were taken from Latimer's compilation

[52] as the most accurate source. Referred to Cs^ these are: 53.8 ± 1.4 kcal/mole

for Li + , 28.9 ±0.9 for Na+, 12.7 ±0.9 for K+.and 6.7 ± 1.1 for Rb+. My previous

calculations [4] were based on values of 54.3, 30.4. 12.7, and 7.7. respectively, which are in good agreement except for Rb+.
Figure 14. Selectivity isotherms for a neutral dipolar site as a function of various charge

distributions and ligand coordination numbers. Described in text.
36 ION-SELECTIVE ELECTRODES

monopolar model, since in this situation the energetic contribution due to the positive pole becomes negligible. Of more interest is the fact that over

a wide range of dipolar charge distributions, the sequences of cation selectivity are essentially the same as those given by the monopolar model (c/. Fig. 10). This is in accord with the experimental observation that a wide variety

of selectivity data for the effects of macrocyclic molecules on artificial membrane systems (as well as on solvent extraction) are characterized by

these very selectivity sequences. Thus, sequence IV (K+, Rb+, Cs+, Na+,

Li+) is observed for nonactin, trinactin, and the cyclic polyether XXXI in Figures 8 and 9. Sequence III has been reported by Mueller and Rudin

[11] and by Lev and Buzhinsky [10] to be characteristic of bilayers ex- posed to valinomycin. Pressman has reported sequence I la for the sol- vent extraction of compound X-537, sequence V for compound X-206

and nigericin, and sequence VII for dianemycin [46] . Sequences III, IV,

and VIII are apparent in Pedersen's published solvent extraction data for

different cyclic polyethers [56]; Lardy and his colleagues have found

similar sequences for the effects of these compounds on biological membranes [57].

It should therefore be apparent that the energies of interaction of cat- ions with the dipolar ligand groups, in competition with the hydration

energies of the ions, can account for the salient features of the selectivity

among the alkali metal cations characteristic of neutral sequestering

molecules.

D. Practical Considerations

From the data of Figures 5, 6, and 8, it is clear that solid ion exchanger

electrodes can have extremely high selectivities for Na+ relative to K+

and moderate selectivities in favor K+ over Na+. Typical liquid ion

exchangers, best known for their usefulness as Ca++ electrodes [7] , can show a K+ to Na+ selectivity in excess of 30 to 1. Neutral carrier systems

offer K+ to Na+ selectivities substantially greater than 100 to 1

.

From a practical point of view, solid ion exchanger electrodes have the

advantage that the ion-detecting sites are truly "trapped," and one does

not have to be concerned with partition equilibria between the membrane

phase and the aqueous solution. Liquid systems, of either the ion

exchanger or neutral carrier type, suffer from the disadvantage that equilibrium for these species must be established between the membrane

and the solution. This problem will probably be less important for neutral

than for charged sites since transient readjustments of the neutral

molecules per se will not contribute directly to the potential. Indeed, it ap- pears likely that the neutral carriers represent one of the ways used by

biological membranes to discriminate among cations [ 14] ; and they offer the possibility that the exquisite selectivities characteristic of living cells can therefore be duplicated in an artificial electrode.
THEORY OF MEMBRANE POTENTIALS 37

VII. Appendix

Derivation of the Equations for tlie Membrane Potential at Zero Current

Although it should be possible to present a general derivation for the

membrane potential, of which each of the three types of membrane elec- trodes discussed in this paper would be a particular case, the three types

of electrodes are physically so distinct that it is more useful to present

separate derivations appropriate to each.

A. Solid Ion Exchanger Membranes

This appendix deduces the expression of the difference of electric potential between two solutions separated by an ion exchange membrane

with fixed monovalent sites and follows the treatment of Conti and Eisen- man [24,25] . The results are valid not only in the steady state for zero net current but also in the non-steady state, being independent of time once

equilibria are established at the boundaries of the membrane. The membrane is assumed to be solely permeable to cations or anions, depending on whether the charge of the sites is — 1 or + 1 , and not to permit any flow

of solvent. Under the assumptions that the difference of standard chemical potentials of any pair of permeant monovalent species and the ratio of

their mobilities are constant throughout the membrane, explicit expressions are derived for the diffusion potential and total membrane potential as functions of time and of solution activities. The expressions are valid

for ideal behavior for any number of permeant monovalent species and for two permeant monovalent species having "n-type" non-ideal behavior.

Consider an ion exchanger membrane interposed between solution (') and solution (") in which the membrane properties vary only in the x

direction, perpendicular to the membrane sufraces. Under the assumption

that the only driving force acting on each species is due to the gradient of

its electrochemical potential, we have at any point in the interior of the

membrane phase:

Ji = -Cm^{tx}\^RT\nai-\-ZiFx\f),i=l,2, . . . N, (Al)

where 7 is the flux per unit area in moles cm-2sec~^ C is the concentration

in moles cm-^, u is the mobility, jjl" is the standard chemical potential, a is the activity, ijj is the electric potential, z is the valence, F the faraday constant, R the gas constant, T the absolute temperature, and the subscript / refers to any one of the permeant species present.

Since any excess space charge is negligible compared to the number of

ion exchange sites at any point:

^z,C,=-zoCo, (A2)

j=i
38 ION-SELECTIVE ELECTRODES

where the subscript 0 refers to the sites. Moreover, conservation of mass

requires:

^--§;.-0,l,...A^. (A3)

The electric current, /, per unit area, is related to the fluxes of the counterions and sites through:

F^zJi = I (A4)

In writing Equation (A4), we assume that there is no electronic contribution to the current. To find the time-dependent solution of Equations (Al) and (A3)

under conditions of current flow is a difficult mathematical problem:

but the behavior of the electric potential at zero membrane current can

be deduced easily as is done below. Non-zero current cases are considered elsewhere [25].

For ion exchanger electrodes such as glass, it is reasonable to assume

that:

and

a ( Ui dx

N. (A6)

Assumptions (A5) and (A6) are certainly satisfied if the standard chemical potentials and mobilities^ are constant.

I will distinguish two cases now. In the first, any number of counterion

species may be present, but their behavior is assumed to be ideal. In the

second, the possibility of a certain type of non-ideal behavior is allowed;

but considerations are restricted to only two different species present. In an ideal system, the activity of any component is equal to its concentration:

ai = Ci; /=1, . . . N. (A7)

On the other hand, for "n-type" non-ideal behavior [24]

:

d\na,ld\nC, = n (A8)

d\na2ld\nC2 = n (A9)

where

4^=0 (AlO)

dx

'For simplicity of nomenclature the asterisks, denoting quantities characteristic of the membrane phase, have been omitted in this Appendix.
THEORY OF MEMBRANE POTENTIALS 39

for membranes whose chemical properties are uniform.

Equation (A 1 ), for the ideal behavior of Equation (A7), reduces to: t)=-Cdx, t)uiix)£[fJi'M+RT\nCi{x, t) ^zF4j{x, 0], ... /V, (All)

where z = 4- 1 or — 1 , depending on whether a cation exchange or anion

exchange membrane is considered. For zero current, Equation (A4)

becomes:

^Jiix, t)=0 (A12)

Addition of Equation (All), taking into account Equation (A5), gives

A dx t-", dx (A13)

Dividing both sides of Equation (A 13) by

gives:

d

'^iii{x)Ci{x, t)

dx t)(A 14)

where numerator and denominator of the right-hand side of Equation

(A 14) have been divided by uiJ Recalling Equation (A6):

^ [fjiUx)+zFiJj{x, t)]^-RT^\nY—Ci{x, t). dx ox Ik (A15)

Equation (A 15) can be seen to be a total differential which is immediately integratible, having a value which depends only on the values

of Ci(x,t) between which it is integrated. Let us take the origin of the x

axis at the boundary between solution (') and the membrane, and let d be

the thickness of the membrane. The electric potential, the standard

chemical potential, and the concentrations, have discontinuities at x = 0 and x=d. I shall indicate by i|/(0,/), />t°(0), C/(0,/) and ijjidj).

^ The expression [Si/, (x)C, (x,0] is positive when the mobility of at least one of the species

is not zero. In Equation (A 14), w,(jc) is assumed to be non-zero.
40 ION-SELECTIVE ELECTRODES

^°(d), Ci{d,t) the values of these quantities at the two boundaries

inside the membrane; whereas by lA' and I shall in- dicate the values of the electric potential and standard chemical potential

in solutions (') and ("), respectively. Integration of Equation (A 15) with

respect to x from 0 to gives the expression of the diffusion potential, Ed = ilj(d,t)-ilj{0,t):

zFEa=^m -iJi\{d)+RT In )

• (A 16)

At the boundary between the membrane and each solution, ther- modynamic equilibrium requires for each species the equality of the elec- trochemical potentials across the interface:

(A 17)

where the superscripts (sol) and (m) refer to solution and membrane.

Disregarding concentration gradients in the solution due to diffusion, Ui

is constant throughout the solution.

Subtraction, term by term, of the first part of Equation (A 17) from the

others gives:

[- } = /<!/; t=l, ... /V (A18)

where Ku is the thermodynamic equilibrium constant of the ion exchange

reaction represented by Equation (4). For / ^ 1 , Equation (A 1 8) together with Equation ( A7) gives, as soon as thermodynamic equilibrium is established at the two boundaries:

)Lt«(0)+/?rinCi(0,0 + 2Fi//(0, t)=iJi^; + RT\na\^zF^'{t), (A19)

fjiT + RT In a'; 4- zFi//"(0 = /x«(^^) + RT In Ci (^7, 0 + zF^{d, t) , (A20)

where a\' and ax" are the activities of component 1 in solutions (') and

("), respectively.

Addition of Equations (A 1 6), (A 1 9), and (A20) gives the expression for the total potential E:

zF zt tti
THEORY OF MEMBRANE POTENTIALS 41

Equation (A 18) at the two boundaries, together with Equation (A7),

gives:

^^Mr7^=KU;i=l, ... .V (A22)

, a; Ci(0, 0

and

a'l Cijd, t) a I Ci{d, t) K'U;i=l. . • ^ N (A23)

as soon as thermodynamic equilibrium is established at the boundaries.

K[i and K'^ refer to the equilibrium constants at the two boundaries.

Taking account of Equations (A22) and (A23), Equation (A21)

becomes: „ y iii ' uT-j^ RT e,u,^^^^^

zF ^ui^„ „•

(^24)

1=1 All expressions through (A24) are valid for two different solvents on

the two sides of the membrane. If the solvent is the same for solution (') and solution ("), then:

lJir = yiT (A25)

and, taking into account Equations (A 18) and (A5):

K'u = K'U = Ku.i=\. ... /V (A26)

so that Equation (A24) becomes simply:

^ u E = ^^A^. , (A27)

which is the desired expression for the membrane potential under ideal conditions.

This equation is time-independent for time-independent solution conditions, once the membrane-solution interfaces have reached equilibrium.

However, it should be noted that if the activities of the ions in solution are varied with time, the total potential will reproduce these time variations.
42 ION-SELECTIVE ELECTRODES

provided they are slow compared to the velocity of establishing the boundary equilibria.

For systems obeying n-type non-ideal behavior, a way of proceeding

similar to that used above gives, taking account of Equations (A8-A10): ^ _ Atf(Q)-/^?(^) ,RT, P(0) nRT^ CAd,t)^f^C,id,t) '~ ^ ^^^''^"IF^'' ' (A28)

zr pya) zt Ci(0. 0 +— ^2(0, 0

for the diffusion potential. For the same solvent in solutions (') and (") the

total potential is given by:

E = —r-r\n . (A29)

Equation (A29) is identical in form to that found characteristic of glass

electrodes by Eisenman [3-6].

B. Liquid Ion Exchanger Membranes

This appendix deduces the steady-state properties of a homogeneous,

ideally permselective. liquid ion-exchange membrane in which sites and

counterions are incompletely dissociated and is based on the analysis of

Sandblom. Eisenman, and Walker [34]. Dissociated species are assumed

to be in chemical equilibrium with neutral ion pairs at every point in the

membrane, their concentrations being interconnected by the law of mass

action. The flux equations, which describe the complete behavior of the

system, are derived by considering the free ions and their combined forms

as separately flowing entities, and the boundary conditions are obtained

by assuming the sites to be completely trapped in the membrane phase

(although free to move within it) while the counterions are free to undergo

ion exchange. Under the restriction of zero membrane current, an expression for the membrane potential is deduced in terms of external solution

conditions and membrane parameters which is valid not only for the

steady state but for certain transient situations as well. The system has been diagrammed in Figure 1 and consists of a membrane separating two homogeneous {e.g., aqueous) solutions whose electric potentials are i//' and i//". The membrane is composed of a single liquid

phase immiscible with the external solutions. In the membrane is dis- solved a ''site'' species, S, bearing a charge ^ ± 1 (given a negative sign

of Fig. 1).^ The sites are assumed to be completely reflected at the boundaries, 0 and d, (as indicated by the arrows), but are free to move within

the interior of the membrane. The system also contains n number of

'Again, asterisks denoting membrane quantities will be omitted in this Appendix.
THEORY OF MEMBRANE POTENTIALS 43

permeable univalent counterion species I whose charge Zi is opposite to that of the sites and which are free to cross the membrane-solution inter- faces as indicated by the arrows in Figure 1 . Any number of co-ion species may be present in the external solutions although the co-ions are as- sumed to be completely excluded from the membrane.

Even species which behave as strong electrolytes in aqueous solutions

will in general not be completely dissociated in a liquid ion-exchange

membrane. Species I and S will therefore be assumed to be in chemical

equilibrium at every point in the membrane with the associated species IS

/+ + S-^/S (Bl)

assuming that the only reactions occuring in the membrane are those in which electrically neutral complexes are formed. For simplicity, considerations are restricted to the smallest complex possible {i.e., the ion

pair).

The chemical potentials corresponding to Equation (Bl) are related

everywhere in the membrane through

IJLi-\- fjis = fjiis; i=l, . . . n (B2)

where /Xi /Xs, and /x/s are the chemical potentials of the counterions, sites,

and ion pairs, respectively. For simplicity, activities will be assumed to be

equal to concentrations. Under this assumption, the concentrations of the

species (C,, Cs, Cs) are related to the association constant, Kis, through a

simple law of mass action

Kis = -§^; i=l, . . . n (B3)

which, in effect, describes a chemical coupling between the various species within the membrane. In addition, the concentrations of the charged

species are coupled electrically through the condition of electroneutrality

Cs^J^Ci (B4)

i

It is useful to consider separately the flows of associated and dis- sociated species. The total flux, of each species through the membrane can be written as a sum of partial fluxes

J7"'=^Ji+Jis (B5a)

Jr'-.h^^Jis (B5b)
44 ION SELECTIVE ELECTRODES

where JJ^\ and JJ^^ are the total fluxes of counterions and sites, Ji and Js are the fluxes of the species in their dissociated state, and Jis are the fluxes of the ion pairs.

Since counterions, sites, and associated pairs are treated as separately

flowing entities, it is possible to write separate linear relationships

between the forces and fluxes of each of the species. By the Curie principle, the chemical reactions introduce no additional driving forces since

the membrane is assumed to be isotropic, and assuming diffusion only in the X direction, the flux equations can therefore be written in the classical manner as: Ji=-UiCi — {RT InC^ + ZiFifj) (B6a)

dx

Js--- UsCs^ (RT In Cs + ZsFilj) (B6b)

ox

Jis = - UisCis ^{RT In Cis) (B6c) ox where Us, w,, and Uis are the mobilities of sites, counterions, and ion

pairs, respectively; Us, Ui and Uis will be assumed to be constant. The continuity equations for the total fluxes and concentrations are: divJ- = —= — (B7a)

where the superscript "Tot" refers to total quantities

(C7»^ = C.-+ C,.;Cr = C. + 2 C-)-

At steady state, the total fluxes are constant, a conclusion which is not

necessarily valid for the partial fluxes. In fact, the partial fluxes are generally functions of distance; and the membrane may be thought of as containing local sources and sinks. Because the continuity equations

apply only for the total fluxes, the number of variables is increased by n

(the number of partial fluxes Jis) over than in the usual Nernst-Planck

treatment. The n additional equations needed to solve the problem are given by Equation (B2).

Assuming that boundary processes are not rate limiting, the boundary

conditions for the counterions follow from the continuity of electrochemical potentials. Hence we may equate the electrochemical potentials of the

counterions across each of the two boundaries 0 and d as
THEORY OF MEMBRANE POTENTIALS 45

RT In al^fJi^-^ziFi}j' = RT In C/(0) + )Lt<)(m) + z,Fi//(0)

;

i=l, . . . n (B8a)

and

RT\n a[' + ^^^+ZiFx\f" = RT In C^^^) + At?(m) +ZiFilj{d);

i=l, . . . n (B8b)

respectively. The quantities on the left-hand sides of Equations (B8a) and

(BSb) refer to the solution phases, while the quantities on the right-hand

sides refer to the membrane phase, and /x°(m) being the standard

chemical potentials in the solution and membrane phases, respectively.

Subtracting any pair of Equations (B8a) and rearranging gives

a'lki a'jkj (B9)

where the constants h and kj are defined as ^/=expl I; A^^=exp( I. (BIO)

Equation (B9) can be written for all the ions

2 ^J^' a[ki a'2k2 a'nkn Ci(0) C2(0) •

• • C„(0) Cs{0) ' (Bil)

where the condition of electroneutrality, Equation (B4), has been used to obtain the last term. From Equation (Bl 1), the membrane concentrations

Ci(0) can be expressed in terms of the solution activity aj as

Ci(0) = Cs{0)x^^- (B12)

i Similar expressions hold for the other membrane boundary.

Subtracting Equation (B8a) from Equation (B8b) gives the expression

for the total membrane potential [E= i//" — ijj'] in terms of internal potential [/^\p=\}j(d) — i//(0)] and the concentrations at the boundaries as ZiFE = ZiFAilj + RT \n-^^-RT In^^ (B13)

Combining Equations (B12) and (B13) yields an expression in terms of

the activities of the counterions in the solutions and ratio of the site concentrations at 0 andd:

£ = A* + ^ln^+ ^ln^—- (BI4)

ZiF C.,(0) ZiF ^(liki
46 ION-SELECTIVE ELECTRODES

This equation will be used to express the total potential in terms of exter- nal conditions and membrane parameters.

The boundary conditions for the sites follow from the assumption that the sites are completely reflected at the membrane boundaries, which

leads directly to the equations:

3 r C]^^'dx=CJ'^' (B15)

and ^-^^

77^^ = 0. (B16a)

Equation (B16a) is valid for all values of x at steady state, but in the

non-steady state it is only valid at the boundaries where

JJ^' (t,0)=J]^^' {t,d)=0. (B16b)

Equation (B15) expresses the condition that the total number of sites contained in the membrane is constant, regardless of their concentration

profile. Expressed per unit area, this number is equal to the average total concentration CJ^^ times the membrane thickness J. Equation (B16a)

states that the total flow of sites must be zero at all points in the membrane in the steady state, whereas Equation (B16b) indicates that for the

non-steady state Jj^^ is zero only at the membrane-solution interfaces. Equations (Bl) to (B16) describe the total behavior of the system. The

special case of the membrane potential at zero current will now be considered. Non-zero current cases are considered elsewhere [58].

Since the electric current / is carried only by the charged species, it is given by . x I = F^zuli + FzJs = Fzi[\Ji-Js) (B17)

substituting Equation (B5) in Equation (B17) yields

I = F^zJ^^' + FzJI'' (B18)

from which it is seen that the electric current is also given by the sum of

the total flows. The potential gradient at zero current can now be ex- pressed by inserting Equations (B6a) and (B6b) into Equation (B17) for

7 = 0 and rearranging to yield

i which can be recognized as the usual expression for the potential gradient

in a "Planck" liquid junction. However, when Equation (B19) is in- tegrated, the presence of ion pairs influences the profiles of Q and Cs. In
THEORY OF MEMBRANE POTENTIALS 47

order to perform this integration it is necessary to derive another expression containing dCsldx.

Combining Equations (B5b), (B6b), and (B6c), = _ j,^Cs {RT In Cs^ ZsFiJj) - Uisds {^i^^Tln ds) ,

and inserting the mass law of Equation (B3),

(B20)

dx ox i OX

UisKisCsdCi

UlsKisCidCs

i dx

(B21)

Equation (B21) is now combined with Equation (B19) to eliminate

dCsldx and solving for the potential gradient,

ZjF di}j RTdx

^ i ' i i By rearranging this equation, the expression is obtained

(B22)

ZjF dijj RT~di

2dCi Hi —

j dx

2 UiCi 2 dCi ^ dCi

dx

RT

where

^ i '

i i

u.d-

(B23)
48 ION-SELECTIVE ELECTRODES

When Equation (B23) is integrated between the two boundaries 0 and

d, the internal potential at zero current, A1//0, is obtained as:

ZiF ^ Ai//o=-ln ^ UiCiid) — td\n ^ iMsKisCi 2

RT dx

(B25)

In order to arrive at an expression for the total membrane potential

at zero current, Equation (825) is combined with the boundary conditions

(812) and (814) to yield:

In-^ \^-[ (B26) RT

where , J2 are the two integrals appearing in Equation (825).

The membrane potential of a liquid ion exchange membrane is there- fore seen from Equation (826) to be composed of three terms, only the

first of which is independent of site distribution. Since no assumption as

to steady state has been necessary in the derivation of Equation (826),

this expression is valid for nonstationary as well as stationary states. In the steady state when, according to Equation (816a), 7/^^ = 0,

Eo is described by the two first terms in Equation (826). Examining the

parameter r, given by Equation (824) and which determines the behavior

of the second term in Equation (825), it is seen that the degree of dissociation enters through the quantity:

(827)

2 "/sC/s The second term is therefore affected by the total concentration of sites,

C7"S since ds and Cs do not vary proportionally when the total number of

sites is changed. This fact is most easily illustrated by adding the mass

laws (83) and inserting the condition of electroneutrality (84). We get

(828)

and from this it is seen that the quantity given by Equation (827) varies

inversely as the concentration of free sites, Cs. As the degree of dissocia-
THEORY OF MEMBRANE POTENTIALS 49

tion is varied, for example by varying Cs from zero to infinity keeping all Kis constant, the quantity / varies from zero to ts, where ts, the trans- ference number of free sites, is given by:

2 UnCi + UsCs (B29)

Consequently, the membrane potential at zero current depends on the site concentrations at intermediate degrees of dissociation. However, when

the degree of dissociation is small and the quantity given in Equation

(B27) is small compared to unity, the potential becomes independent of

the degree of dissociation. In the Hmiting case of complete dissociation, I is zero (/ = 0) and

f ^

since I is also zero in the steady state, the potential is described by the

first term of Equation (B26) as y UikaIn 2 ^^i^'i (B30)

In the special case of strong association for two counterion species,

Equation (B27) is much less than unity; and the integral in Equation

(B26) can be written as

uisC]K\s = ^^-^ d\n

{Ui-\-lls) TtH- W2-\-Us

t/2 Ui 77-+ U-l ^2

(B31)

where the condition of electroneutrality has been taken into account and

where we have divided through by C2. The only independent variable is now C1/C2 and the integral can be solved explicitly to give:

I. ^ {ui^Us)Q id) 2 ^-KisCiid) ^ UiCiid)

(1-t) In^^;^ + T In V -In
50 ION-SELECTIVE ELECTRODES

Equation (B32) depends only on the values of d of the boundaries and is therefore profile independent, which has important consequences to be

discussed below.

When the boundary conditions are inserted in Equation (B32) combined with Equation (B26), taking into account that J = 0 in the steady

state since Jj'^^ = 0, then the total potential is:

2 2 ^ {ui-\- Us)kia' 2 UisKiskia'l ^E=il-r)\n'^ +Tln -~ (834)

2 {ui-\-Us) kia'l 2 UisKiskia'l

i=l i=l Note that Equation (B34) has been derived using only the condition that

JJ*^^ = 0 and'does not require the counterions to be in a steady state. Despite the many studies of the electrode properties of liquid ion

exchangers, none of the measurements published to date appear to cor- respond to the convection-free steady state considered to this point. This

is because the membrane phase has either been deliberately stirred or because precautions to prevent convective mixing in its interior have not been taken (the membrane phase being so thick that steady states have

generally not been reached and because, moreover, stable concentration

gradients can only be established in the relatively static layers just inter- nal to the solution interfaces).

From Equations (Bl 1), (B15), and (B16), it is seen that a simple dilu- tion of the external solution on one side of the membrane will not alter the

interior concentrations. The first two terms in Equation (B14) are there- fore unaltered by such a dilution; and the potential will vary with the Nernst slope as given by the third term. This behavior is a consequence

of assuming complete co-ion exclusion and completely trapped sites. Since Equation (B14) is valid at all times, this has the practical con- sequence that the membrane potential will respond in a step fashion to a

step change in solution conditions whenever this corresponds to a simple

dilution. Except for the above case, however, a step change in external solution

conditions will be accompanied by a redistribution of the sites until a new

steady state is reached. However, when a step change is made from a

previous steady state, the profiles are initially unaltered. 7J"^ is therefore zero in the interior of the membrane at zero time. At the boundaries,

yj"^ is zero at all times by virtue of the boundary conditions (B16b).

Therefore of Equation (B26) is zero instantaneously following a step

change in solution conditions. Since in the limit of complete dissociation,

of Equation (B26) is zero; while in the limit of strong association,
THEORY OF MEMBRANE POTENTIALS 51

is a profile independent [being given by Eq. (B32)] , we reach the important practical conclusion that the instantaneously observed potential is given by the steady state expression (B26) for the case of complete dis- sociation as well as by Equation (B34) for the case of strong association.

This conclusion is true not only for convection-free systems but also for

stirred systems because is independent of the concentration profiles.

If the membrane interior is deliberately stirred, a quasi-steady state of

potential will be rapidly established [again described by Eqs. (B26) and

(B34)] since in this case Jis zero because the uniform distribution of

sites in the stirred interior reduces to zero therein.

C. Neutral Carriers

This appendix deduces the electrical properties of a thin liquid (e.g., hydrocarbon) membrane, interposed between two aqueous solutions, and

containing uncharged molecular carriers for ions and is based upon the

theoretical treatment of Ciani, Eisenman, and Szabo [13,38]. The analysis is carried out within the framework of classical electrochemistry but

without making any assumptions as to electroneutrality or as to profiles

of concentration or electric potential within the membrane.

The system and its reactions has been diagrammed in Figure 3. For the

reaction, Equation (19), of a neutral macrocyclic molecule, S, with a positive monovalent cation, I+, to form a charged complex, IS+, the equilibrium constant in a given homogeneous phase (e.g., aqueous or organic) is defined by:

RT J aias V exp (CI)

where v is the mean molal volume; au ch, and a is denote the activities at equilibrium in moles per liter; and /x° , /x ° , and />t°s are the standard

chemical potentials of the cation, neutral site, and charged complexes,

respectively. The charged complex IS+ can react further with a monovalent anion, X-, to give a neutral compound ISX through reactions. Equation (21), whose equilibrium constant is:

V exp RT

(li (C2)

Therefore, if n species of monovalent cations and m species of monovalent anions are present in a homogeneous solution containing a given

concentration of neutral compound, the chemical reactions occurring in the system will be characterized by n constants K,,- (/= 1 ,2, . . ., and n-m constants Kisx (/= 1 ,2 . . n; x= \ ,2, . . ., m). If the activities are
52 ION-SELECTIVE ELECTRODES

known functions of the concentrations, the system of Equations (CI) and

(C2) allows us to determine the composition of the phase in terms of the

equilibrium constants of the reactions and of the given amounts of elec- trolytes and neutral carriers initially contained in the system.

When considering the equilibrium between two separate phases, it is convenient to define the partition coefficient of each component /i, bearing a charge zn, namely:

V— exp

f^h-f^r ar, z„F jip* - ijj) 0 _ ,,0*'

til /i.f'iiri III I (C3) RT —a, exp

an RT

where an and an designate activities, v and ?;* are the mean molal

volumes, and i//*— i//is the potential difference between the two phases (the

* being used for the organic phase). Note that each component h cor- responds to one of the species of ions or complexes in the system (e.^.,I+,

S, IS+, ISX, X-) and that for uncharged species (for which Zh = 0) the

third term of Equation (C3) reduces to atI an. For a planar membrane diagrammed in Figure 3 interposed between

two solutions of differing composition with the x-axis directed perpendicularly to the interfaces and parallel to the direction of the fluxes, we

denote the x-coordinates of the membrane boundaries by 0 and d. An as- terisk will be used to denote the membrane phase, while superscripts (') and (") will refer to the aqueous solutions. It is assumed that: (i) the rate of diffusion is controlled by the diffusion across the membrane; (ii) the

ionic complexes IS+ are the predominant charged species in the membrane so that the contribution to the electric current due to the partial

fluxes of free ionic species {e.g., I+, X-) can be neglected; and (iii) the activities of the species IS+ in the membrane are assumed equal to concentrations. The validity of assumption (ii) and the consequent lack of elec- troneutrality in the membrane is justified from the theory of interaction

between double layers when the partition coefficients of the ionic complexes are much higher than those of the free ionic species and when the

thickness of the membrane is on the order of or less than the Debye length

of the membrane phase [38].

From assumpfions (i), (ii), and (iii) and recalling the definition, Equation

(C3), the confinuity of the electrochemical potentials of the species IS+ at the interfaces gives:

C.(0) = „: exp^I*^^p)i; , = 2, . . . « (C4)

and

CUd) = aLh. exp ^^'''"^^ /= 1, 2, . . . n. (C5)
THEORY OF MEMBRANE POTENTIALS 53

Describing the fluxes of the species IS+ by the Nernst-Planck equations, the condition of zero current requires:

0 =

f = g^S= -«^2«<t^+C*^^) (C6)

where ufg are the mobilities of the charged complexes in the membrane

in moles cm^ sec-^ joules-^ Assuming constant mobility ratios, Equation

(C6) can be integrated immediately, without further assumptions to give an explicit expression for the "internal potential" of the membrane:

r{d)-nO)=-^\n ^

(C7)

i=l Substituting C/5(0) and C^^id) by the right-hand sides of Equations

(C4) and (C5) we find that it is not necessary to solve explicitly for the in- ternal potential since the (observable) total membrane potential is given directly by:

E = r-^'=-jr\n-^——- (C8)

i=l which shows the simple dependence of E on the aqueous activities of the

complexed cations, flJs'and a'lg. Since these activities are not known, it is desirable to express this result

explicitly in terms of the (given) aqueous concentrations of salts and complexing molecules. For the case in which only two species of cations, 1+ and J+, are present, both at higher concentrations in the aqueous phases

than the neutral species

Gi > CI«^ and aj > C]^' (C9)

where CJ^^ indicates the total concentration of S in the aqueous phase

and the inequalities (C9) are assumed to be satisfied in both solutions. Recalling that

ni m Cs — CJ°^ Cis Cj.s 2 Cisx 2 Cjsxi (C 1 0)

x=\ J-=l restricting considerations to the same total concentration of S in both

aqueous solutions, and solving the system of Equations (CI) and (C2)

under the additional assumptions that: (iv) the species S and IS+ behave

ideally in the aqueous solutions, and (v) that the concentration of the
54 ION-SELECTIVE ELECTRODES

neutral complexes ISX and JSX are negligible in water, Equation (C8)

becomes:

£ = -prln

a'i +

RT l^Ktsa'r

(Cll)

where a, and Oj are the activities of two monovalent cations, 1+ and J+ in solutions (') and ("). The second term of Equation (Cll) is negligible when there is negligi- ble complex formation in the aqueous solutions (as, for example, when the

ionic concentrations in solutions are sufficiently low). In this situation. Equation (Cll) reduces to the very simple form:

RT a- +

In (C12)

Note that the bracketed selectivity parameter depends on such parameters as the mobilities of the charged complexes in the membrane (wj^, ufg) their partition coefficients {kjs, kis) and their association constants

in the aqueous solutions (Kf^ ,Kts) .

VIII. Acknowledgment

This work has been carried out under the generous support of the National Science Foundations (Grants GB 4039, and GB 6685) and of the

National Institutes of Health (Grant GM 14404-01/02/03).

IX. References

[ 1 ] Cremer, M., Z. Biol. 47, 562 ( 1 906).

[2] Haber, F.,and Klemensiewicz, Z., Z. Physik. Chem. (Leipzig) 67, 385 (1 909).

[3] Eisenman,G., Rudin, D. O., and Casby, J. U., Science 126,831 (1957).

[4] Eisenman,G., Biophys. J. 2, part 2, 259 ( 1962).

[5] Eisenman, G., in Advances in Analytical Chemistry and Instrumentation 4, C. N.

Reilley,Ed.,Wiley-lnterscience,N. Y., 1965, p. 215.

[6] Eisenman, G., Ed., Glass Electrodes for Hydrogen and Other Cations: Principles and Practice, Marcel Dekker, N. Y.,1967.

[7] Ross, J. W., Jr., Science 155, 1378 (1967).

[8] Ross, J. W., Jr., Orion Research Inc., Bulletin 92-8 1

.

[9] Frant, M., and Ross, J. W., Science 154, 1 553 ( 1 966); Orion Research Bulletin 94-09 and 94-16.

[10] Lev, A. A., and Buzhinsky, E. P., Cytologia (U.S.S.R.) 9, 106(1967).

[II] Mueller, P., and Rudin, D. O., Biophys. Biochem. Res. Comm. 26, 398 ( 1 967).
THEORY OF MEMBRANE POTENTIALS 55

[12] Stefanac,Z.,andSimon, W., Microchem. J. 12, 125(1967).

[13] Eisenman,G.,Ciani,S.,andSzabo,G.,Fed. Proc. 27, 1289(1968).

[14] Eisenman, G., Szabo, G., and Ciani, S., Proc. of the Coral Gables Conf. on the Physical Principles of Biological Membranes, Dec. 18-20, 1968, Gordon and

Breach, Science Publisher (in press). [15] Eisenman, G., Ann. N. Y. Acad. Sci. 148,5 (1968). [16] Planck, M., Ann. Physik. Chem. 39, 161 ( 1 890); 40, 56 1 (1890). [17] Nernst,W.,Z. Physik. Chem. 2, 6 1 3 ( 1 888); 4, 129(1889).

[18] TeorelKT., Proc. Soc. Exp. Biol. Med. 33, 282 ( 1 935).

[ 19] Teorell, T., "Transport processes and electrical phenomena in ionic membranes" in Progr. in Biophys. & Biophysical Chem. 3, J. A. V. Butler and J. T. Randall, Eds., Pergamon. N. Y., 1953. [20] Meyer, K. H., and Sievers, J. F., Helv. Chim. Acta 19, 649 ( 1936). [21] Helfferich, F.. Disc. Faraday Soc. 21, 83 ( 1 956). [22] Mackay, D., and Meares, P., Kolloid-Z. 171, 139 (1960). [23] Karreman,G.,and Eisenman, G., Bull. Math. Biophys. 24, 4 1 3 (1962). [24] Conti, F., and Eisenman, G., Biophys. J. 5, 247(1965).

[25] Conti, F., and Eisenman, G., Biophys. J. 5, 51 1 (1965). [26] Stephanova, O. K., Shultz, M. M., Materova, E. A., and Nicolsky, B. P., Vestn.

Leningr. Univ. 4, 93 (1963). [27] Doremus, R. H., "Diffusion Potentials in Glass" (Chapt. 4 of Ref. [6] ). [28] isard, J. O., "The Dependence of Glass-Electrode Properties on Composition"

(Chapt. 3 of Ref. [6]). [29] Doremus, R. H., "Ion Exchange in Glasses" in Ion Exchange 2, J. A. Marinsky, Marcel Dekker, N. Y., 1969.

[30] Haber, F., Ann. Physik. 26, 927, (1908). [31] Shean, G. M., and Sollner,K., Ann. N. Y. Acad. Sci. 137, 759 (1966). [32] Eisenman, G., Anal. Chem. 40, 3 10 ( 1968). [33] Conti. F., and Eisenman, G., Biophys. J. 6, 227 ( 1 966). [34] Sandblom,J. P., Eisenman, G., and Walker, J. L.,Jr.,J. Phys. Chem. 71, 3862 (1967). [35] Moore, C, and Pressman, B. C, Biochem. Biophys. Res. Commun. 15, 562 (1964). [36] Pedersen, C. J., J. Amer. Chem. Soc. 89, 70 1 7 ( 1 967). [37] Mueller, P., Rudin, D. O., Tien, H. T., and Wescott, W. C. Circulation 26, 1 167

(1963). [38] Ciani, S., Eisenman, G., and Szabo, G., "A Theory for the Effects of Neutral Carriers such as the Macrotetralide Ac'tin Antibiotics on the Electrical Properties of

Bilayer Membranes", J. Membrane Biol. 1, 1 (1969). [39] Eisenman, G., Ciani, S., and Szabo, G., "The Effects of the Macrotetralide Actin

Antibiotics on Equilibrium Extraction of Alkali Metal Salts into Organic Solvents"

J. Membrane Biol, (in press). [40] Szabo, G., Eisenman, G., and Ciani, S., "The Effects of the Macrotetralide Actin

Antibiotic on the Electrical Properties of Phospholipid Bilayer Membranes", J. Membrane Biol, (in press). [41] Eisenman, G., "The Origin of the Glass Electrode Potential" (Chapt. 5 of Ref. [6]). [42] Truesdell, A. H., and Christ, C. L., "Glass Electrodes for Calcium and Other

Divalent Cations" (Chapt. 1 1 of Ref. [6] ). [43] Rechnitz, G. A., "Cation-Sensitive Glass Electrodes in Analytical Chemistry"

(Chapt. 12 of Ref. [6]). [44] Eisenman, G., unpublished data. [45] Lardy, H. A., Graven, S. N.,and Estrada-O, S., Fed. Proc. 26, 1355 (1967). [46] Pressman, B. C, Fed. Proc. 27, 1283 (1968).
56 ION-SELECTIVE ELECTRODES

[47] Lev, A. A., Buzhinsky,E. P., and Grinfeldt, A. E., Proc. 24th Int. Congr. of Physiol.

Sci. 6, 39(1968).

[48] Simon, W., personal communication.

[49] Tosteson, D. C, personal communication.

[50] Eisenman, G.. in Symposium on Membrane Transport and Metabolism, A. Klein- zellerand A. Kotyk, Eds., Academic Press, N. Y., 1961, p. 163. [51] Eisenman, G., Proc. 23rd Int. Congr. of Physiol. Sci.; Exerpta Medica 87, 489

(1965). [52] Latimer, W. M., The Oxidation States of the Elements and Their Potentials in Aqueous Solutions, 2nd Ed., Prentice-Hall, N. Y., 1952. [53] Reichenberg, D., "Ion-Exchange Selectivity" in Ion Exchange 1, J. A. Marinsky,

Ed., Marcel Dekker, N. Y., 1968, p. 227.

[54] Sherry, H. S., "The Ion-Exchange Properties of Zeolites" in Ion Exchange 2, J. A. Marinsky, Ed., Marcel Dekker, N. Y., 1969, p. 89. [55] Diamond, J. M., and Wright, E., Ann. Rev. Physiol. 31, 58 1 (1969). [56] Pedersen,C. J., Fed. Proc. 27, 1305 (1968). [57] Graven, S. N.. Lardy, H. A., Johnson, D., and Rutter, A., Biochem. 5, 1729 (1966). [58] Sandblom,J. P., Eisenman, G., and Walker, J. L.,Jr.,J. Phys. Chem.71, 387 1 (1967).
CHAPTER 2

SOLID-STATE AND LIQUID MEMBRANE

ION-SELECTIVE ELECTRODES

James W. Ross, Jr.

Orion Research, Incorporated

Cambridge, Massachusetts 02139

I. Introduction In this paper I will summarize the work, carried out in our laboratory

by myself and Dr. Martin S. Frant, which has been directed toward

developing useful new ion-sensing devices. I will not attempt to give a complete survey of the ion-selective electrode field and will omit the important class of glass membrane electrodes and the newer heterogeneous

membrane devices, which are discussed in Chapter 3.

II. The Practical Importance of Ion Activity Measurement

Our work was undertaken in response to a change in the type of

question being asked of an analytical chemist. Historically, the analyst was expected only to count atoms of a given kind in a sample; i.e., to determine concentration. The bulk of the subject matter of classical

chemical analysis has been concerned with this problem. Concentration

data is, of course, very useful and will continue to be needed. In many

cases, however, when one is interested in positions of chemical equilibria or rates of chemical reaction, predictions based on concentration information can be misleading.

To take a particularly simple case, zinc dissolves rapidly in hydrochloric acid, but is relatively unaffected by an acetic acid solution of the same

concentration. Attempts to correlate acid concentration with corrosion

rates will be disappointing. If, instead of acid concentration, the pH —

that is, the hydrogen ion activity in the acid solution — is measured,

the correlation with corrosion rates will be excellent. The role of

hydrogen ion activity in acid-base chemistry has been appreciated for years, and its importance led to the development of the first ion-selective

electrode, the familiar glass membrane pH electrode. In recent years, there has been a growing awareness that activity measurements are equally important for other chemical species. The hardness

of water depends on the calcium ion activity in the sample, and not on the

total calcium concentration. The role of calcium in biological processes

57
58 ION-SELECTIVE ELECTRODES

such as nerve conduction, muscle contraction, and blood clotting is deter- mined by the free calcium ion activity in the system, which may vary by

several hundred percent from the total calcium concentration. Other ex- amples involving other ions are easy to find. In general, if an analysis is being performed in order to answer a question relating to a rate of a chemical reaction or the position of a chemical equilibrium, it is an activi- ty measurement, rather than a concentration measurement, which will be

most significant.

III. The Ideal Nernst Electrode

Practical measurement of ion activities can be accomplished by several

techniques. One method is to measure the effect of an ion on the rate of some calibrated process. Calcium ion activities, for example, have been

measured in serum samples by noting the beating rate of a freshly excised

frog heart immersed in the sample. In principle, pH could be determined

by measurement of rates of hydrogen evolution from a standard metal sur- face. Apart from the inherent inconvenience of such methods, they are in- variably subject to numerous interferences, and the fact that they have

been used at all underscores the importance of ion activity measurement.

Oxidation-reduction processes occurring at the surface of metal elec- trodes permit activity measurements of a limited number of ions. Such

electrodes are subject to many interferences and have not found wide ap- plication as sensing devices. They are widely used as reference elec- trodes, however, in the form of the familiar calomel and silver-silver chloride half cells. The only device capable of determining ion activities which is both con- venient and at the same time sufficiently free from interferences to be of

general usefulness is the ion-selective membrane electrode (Fig. 1). The

sensing membrane allows only the ion of interest to pass from the sample

solution at the outer membrane surface to an internal solution in contact with the inner membrane surface. The internal solution contains a fixed

activity of the ion to which the membrane is permeable.

When such an electrode is placed in a sample solution, there is a momentary flux of ions across the membrane in the direction of the solution

containing the lower activity of the mobile ion. Since the ions carry a

charge, an electrical potential is set up which opposes further ion migration, and eventually an equilibrium is established in which the potential across the membrane is exactly that required to prevent further net move- ment of ions. Changes in this membrane potential can be measured by making electri- cal contact to the inner solution with a suitable reference electrode, and

at the same time contacting the sample solution with a second reference
SOLID-STATE AND LIQUID MEMBRANE ELECTRODES 59

ION-SELECTIVE ELECTRODE

IILVER OR CALOMEL

HALF CELLS EXTERNAL

REFERENCE

ELECTRODE

SELECTIVE MEMBRANE LIQUID JUNCTION SAMPLE SOLUTION

Figure 1 . Schematic diagram of the apparatus used in ion-selective electrode measurement.

electrode via a salt bridge. A high input impedance voltmeter connected

across the two reference electrode leads will indicate a potential given by

the Nernst equation: = constant

+

^'^^"^log^ (1) zr Here E is the potential, in millivolts, developed by the system. The constant term depends on the particular choice of reference electrodes used, on the choice of ion activity in the inner solution, and also includes a small

potential associated with the liquid-liquid junction at the salt bridge connection. RTIF is the Nernst factor, which depends on the temperature,

and has a value of 59.16 millivolts at 25 °C. A is the activity (in the sample solution) of the ion to which the membrane is permeable, and z is its charge, including sign. In use, the electrode pair must first be calibrated with standard solu- tions of known activity (the calibrating buffer solutions, in the case of pH

measurement). A plot of electrode potential vs. \ogA of the standard solu- tions can then be used as a working curve to determine unknown sample

activities. Instruments are also available with which direct activity

readings can be obtained from the meter scale, eliminating the need of

plotting a working curve.
60 ION-SELECTIVE ELECTRODES

rV. Advantages and Disadvantages of Electrode Methods

Compared with other analytical techniques, an electrode measurement

has an impressive list of advantages. Although an electrode senses ionic

activity, it can also be used to determine free ion and total concentrations

through methods such as titration, standard addition, and ionic strength

buffering. These approaches to concentration measurement are discussed

in subsequent chapters, and I mention them here only in passing.

Electrode measurements are rapid— virtually instantaneous in many

cases. Time responses are frequently as fast as ten milliseconds, and

even under unfavorable conditions, a reading can be obtained within

two minutes. They therefore find ready application in such areas as

kinetic studies and process control. An electrode measurement is nondestructive. The number of ions

transported across the membrane in order to establish the equilibrium

potential is infinitesimal relative to the number present even in the most

dilute samples. In addition, with appropriate electrode geometry, very

small samples amounting to a few tenths of a milliliter can be handled.

These advantages can be very important in biological applications, where

several determinations must be performed on a single small sample.

In most cases, no sample pretreatment is necessary. Opaque solutions

and even viscous slurries can be measured directly. Time-consuming fil- tration and distillation operations are eliminated. Automated analytical

methods based on electrode measurements are therefore extremely simple to design.

Finally, the equipment required is simple and. at least when compared

with most analytical methods of analysis, relatively inexpensive. Portable

battery-operated meters are available which can be used in such applications as geological prospecting, oceanography, and water pollution

control. Unfortunately, at their present state of development, electrodes are not

highly accurate devices. All electrodes exhibit a drift in the magnitude of

the constant term in the Nemst equation at a rate which depends primarily on the temperature variation in the surroundings. An electrode in an

average laboratory will show a noncumulative drift of about two millivolts per day. Under field conditions or in process control applications, even

larger fluctuations can occur. The presence of drift requires periodic

restandardization at a frequency which depends on the accuracy required

and the rate of temperature variation. Under the most favorable conditions, in an air-conditioned laboratory with samples and standards all at the same temperature, a precision of 0.2 millivolt can be obtained on

replicate measurements of the same sample. Under typical field conditions, a precision of 4.0 millivolts is more usual. The following table trans-
SOLID-STATE AND LIQUID MEMBRANE ELECTRODES 61

lates the uncertainty in potential into the corresponding percent uncertainty in ion activity as determined from the Nernst equation.

Precision in E Percent uncertainty Percent uncertainty

monovalent ion divalent ion

0.1 mV 0.4 0.8 2.0 mV 7.5 15.0

For a given uncertainty in E, the precision of a divalent ion measurement

is poorer than that of a monovalent ion because of the appearance of the

charge, z, in the Nernst equation. These figures apply only to direct elec- trode measurements. When electrodes are used as end-point detectors in

titrations, precisions of better than one part per thousand are possible.

Being a logarithmic device, an electrode gives a constant precision

throughout its dynamic range. Trace ion levels in very dilute solutions can

therefore be determined with just as high accuracy as for concentrated

solutions.

Another problem in electrode measurements is the uncertainty as- sociated with the definition of ion activity. By ion activity, we intuitively mean the "effective concentration" of the free ion in solution. This "effective concentration" is different from the total concentration because of

the presence of complexes and ion-pairs, and also because of the effect of

sample ionic strength. At the present time, there is no known way by

which the activity of an ion in a solution of known composition can be cal- culated or measured to a high degree of accuracy. In other words, it is presently impossible to formulate with accuracy the standard solutions

necessary to calibrate an electrode without making some arbitrary as- sumptions. The problem has already been faced in the case of pH measurements, and resulted in the development of the conventional NBS pH

scale and standard buffer solutions. Similar work must also be carried out

for the other ions for which electrodes are now available. This problem is the subject of Chapter 6, and I shall say no more about it here, except to emphasize the importance of this work to the field of applied electrode

analysis. V. Liquid Membrane Systems

A. General Properties

From the preceding discussion, it is evident that all ion-selecfive elec- trodes are similar in mechanism and in the way that they are used. They

differ only in the details of the process by which the ion to be determined moves across the membrane and by which other ions are forbidden access

to the membrane phase.
62 ION-SELECTIVE ELECTRODES

In discussing membranes, it is useful to separate the transport process

of an ion through the membrane into two steps; the movement of the ion

within the membrane phase, and the process by which the ion enters the

membrane. It is obviously necessary that the ion to which the membrane

is permeable be able to both enter the membrane and move. Rejection by

the membrane of other ions can be achieved by blocking either the move- ment or the ability to pass the membrane-solution interface, or both.

A liquid phase offers one approach to a membrane material. The

problem of insuring mobility of the sought-for ion is immediately solved,

since if the ion is capable of existence in the membrane at all, it will be

free to move by diffusion. Any selectivity of the liquid phase will, of

necessity, have to be based on entering restrictions at the interface. Since

the liquid phase will be in contact with aqueous solutions, it must be

water-insoluble, and it must also have a low enough vapor pressure to prevent significant evaporation. The liquid phase, in effect, should be a

relatively low dielectric-constant, high molecular-weight organic liquid.

Two solutions to the mechanical problem of providing a stable liquid

membrane separating two aqueous solutions are shown in Figure 2. In the

first configuration, which was used in our earlier work [1 ]

, the membrane

Hquid is held inside a glass tube sealed across the end with cellulose dialysis membrane. The dialysis membrane is equally permeable to all ions and

serves only to prevent loss of the organic liquid phase. The internal aque- ous electrolyte solution is provided in the form of a small tube filled with an agar gel and provided with a silver-silver chloride reference electrode.

O.IMCaClg AGAR GEL

LIQUID ORGANIC EXCHANGER

CELLULOSE DIALYSIS MEMBRANE

0.1 M CaClg

I00m>i PORE DIAMETER ACETATE FILTER DISC

Figure 2. Liquid membrane electrodes, (a) A simple configuration suitable for work where

high resistance and long time response are not important, (b) A thin layer configuration with low resistance and fast time response.
SOLID-STATE AND LIQUID MEMBRANE ELECTRODES 63

The actual electrode membrane, across which changes in cell potential

arise, is represented by the organic liquid in the region between the dialysis membrane and the agar gel. Such electrodes are characterized by a

high resistance and a relatively long time-response, due principally to the

thick layer of the organic phase.

An improved but more complicated assembly is also shown, in which

the organic liquid is held in the pores of a thin (0.076 mm) disc of

Millipore filter membrane of about 100 nanometer (millimicron) pore

diameter. If treated to render the filter material hydrophobic, the organic

liquid will wick into the pores of the membrane from a reservoir provided

in the annular space indicated in the diagram. The central chamber is filled with the internal aqueous electrolyte and a reference electrode. An

electrode of this type has the advantage of a very thin membrane phase,

while at the same time it is able to tolerate pressure differentials of greater

than one atmosphere without rupture or displacement of the organic

phase from the pores. Since an ion cannot exist by itself in the liquid membrane phase without

violating the requirements of electroneutrality, it is necessary to provide

a charged "site" of opposite sign as an addition to the solvent liquid. The

ion and the site are dissolved as neutral, essentially undissociated salt molecules in the base solvent. The site ion must have a relatively high

molecular weight to insure that the resulting salt will be substantially in- soluble in water. In addition, the salt must be soluble in the low dielectric constant solvent. Organic phase solubility can usually be obtained by

providing long hydrocarbon-chain groups on the site ion. In a liquid membrane system, the site and the ion move together

through the membrane phase. At the membrane interface, a process of ion

exchange can take place between the ions of the ion-site salt in the organic

phase and the free ions in the aqueous phase. The selectivity of the elec- trode depends primarily on the selectivity of this ion exchange process. In order for the electrode to display Nernstian response to an ion A++ in the

presence of an interfering ion B++, it is necessary that the position of the

following equilibrium lie far to the left. B++ + AR2 ^BR., +A++ (2) R represents the charged "site" group. Putting this in other terms, selectivity requires that the site R form a more stable complex with the

sought-for ion than with any potentially interfering ion in the sample. To

the extent that B++ enters the membrane phase (and this will always be

the case if the activity of A++ in the sample is sufficiently low relative to the activity of B++), then the electrode potential will be affected; i.e., B++

will be an interference.
64 ION-SELECTIVE ELECTRODES

The theoretical treatment of a liquid membrane system in which two or more ions are simultaneously transported is difficult. Eisenman [2] has

solved the problem for a few special cases, but it should be pointed out

that the analytically useful systems which will be discussed in this section

are much more complicated than the systems which have been accessible

to mathematical analysis. Any theoretical equations based on integration

of the Nernst-Planck flux equations applied to monomeric site-ion molecules of symmetrical charge type will be approximate at best when

applied to real electrodes.

Fortunately, the analytical chemist is only interested in electrodes

which behave in a simple Nemstian manner in response to the ion activity levels present in his sample. The absence of exact equations describing

non-Nernstian mixed-ion potentials is not a serious disadvantage. It is important, however, to be able to predict in advance if a given electrode will be subject to interference in a given sample. For this purpose, the following empirical equation is useful:

Here A and B represent the sample activity levels of the sought-for ion

and an interfering ion, respectively. The activity of each interfering ion in the sample, raised to a power equal to the charge ratio, is multiplied by a weighting factor, the selectivity constant ku If the resulting terms are

negligible compared to the activity of A. then the electrode may be used

with confidence. The equation has been tested with a wide variety of elec- trodes and a large number of interfering ions, and agrees quite well with

experiment at low levels of interference. However, the equation is only

approximate when the interference levels are high, and it should not be

used in an attempt to correct a potential measurement for interferences

when the activity levels in the sample are known. However, it does permit

the analyst to calculate in advance, given a table of selectivity constants,

the maximum level of interfering ions which can be tolerated before inter- ference becomes serious. In attempting to develop a new electrode for a given ion, it is first necessary to find a site group which displays the required selectivity,

given the interfering ions which are likely to be present in the sample. The

best guide in searching for a new site type is the value of the complex ion

stability constant for various ligands with the ion of interest. For a given

ligand, the ratio of the stability constant for the ion of interest to that of a

potentially interfering ion in aqueous solution will be approximately the same as the ratio in an organic phase. If the ratio is large, then the ligand,

suitably substituted to confer organic-phase solubility to the ion-ligand

salt, will in all probability make an electrode showing good selectivity

E= constant -(- 2.ZRT

log A + ;^ A-,BfB/-A (3)
SOLID-STATE AND LIQUID MEMBRANE ELECTRODES 65

in the presence of the interference. In addition to selectivity requirements, the site group must also be capable of entering into a rapid,

mobile ion exchange equilibrium with the ion of interest. Many groups

which are potentially interesting from a selectivity standpoint, such as most multi-dentate chelating sites, equilibrate too slowly to give elec- trodes with reasonable time responses. In addition, most of these chelat- ing groups form mixed complexes with the ion of interest and hydrogen

ion over the pH range which is of major analytical interest. Hydrogen ion

in this situation will be transported across the membrane, producing a

large hydrogen ion interference.

With these guides in mind, it is usually possible to find several site groups among the vast number of known complexing ligands showing the

required selectivity, provided that the number of potential interferences

is reasonably small. It is unlikely that a completely selective electrode will ever be found that can be used in every sample solution. The chances of

finding a system which will be sufficiently selective in a given restricted

application are, however, quite good.

A few comments regarding the solvent should be made. Most of the

ion-site complexes of practical interest are bulky molecules in which the

ion is well shielded from interaction with the solvent. As a result, the

choice of the solvent has little effect on electrode selectivity. In the case

of divalent ion selective systems based on phosphoric acid ester groups, we have found that some differences of selectivity among the various

alkaline-earth ions can be achieved by varying the polarity of the solvent. In general, however, the solvent is merely an inert vehicle for site-ion dif- fusion, and its selection is made on the basis of the physical properties

mentioned earlier. B. Phosphate Ester Systems

Some of the first systems we studied were ion-site salts derived from di- esters of phosphoric acid [1]. We were searching for an electrode which

would show good selectivity for calcium ions in the presence of large

amounts of sodium and lower levels of potassium and magnesium. An

electrode of this description was needed for biological research and in water quality analysis. The choice of the phosphate ester was made

because phosphate and polyphosphate ions form stable complexes with

calcium, while no such complexes are known with sodium and the alkali metals. In addition, esters of phosphoric acid containing long hydrocarbon chains are easy to synthesize. A diester, rather than a monoester,

group is necessary to avoid the problem of mixed complex formation with

hydrogen ion mentioned earlier. Electrodes made from diesters with

hydrocarbon chains in the Cs-Cin range showed good selectivity for calci- um in the presence of sodium, as expected. In solvents with very polar
66 ION-SELECTIVE ELECTRODES

substituent groups, such as dioctylphenylphosphonate, the electrodes

also showed good selectivity for calcium relative to magnesium and other

alkaline-earth ions. Selectivity in the presence of other divalent ions —

Zn++, Pb+ + , Fe++, ^rc — was poor, but these ions are not normally

present in the samples in which the electrode was intended to be used.

Using less polar solvents, such as decanol, electrodes were obtained

which showed virtually identical response to all the alkaline-earth ions,

while still preserving good rejection of monovalent ions. Electrodes of

this type are useful for the determination of water hardness.

A calibration curve of an electrode in CaCL solutions is shown in Figure 3. This particular electrode was made from a liquid phase containing O.IM calcium salt of didecyl phosphoric acid in dioctylphenylphosphonate. In converting calcium ion concentrations into activities, we have used the ionic activity coefficients of Kielland [3], which were

obtained by the use of an extended Debye-Hiickel equation.

Over the range lO-i to lO-^M, this electrode behaves in a completely

Nernstian manner. Below lO'^M, the calibration curve forms a plateau,

and the electrode no longer responds to changes in sample calcium ion activity. This lower Hmit of detection is caused by the small solubility of the

calcium-phosphate ester salt in the aqueous phase. In very dilute sample

solutions, the electrode saturates the sample, raising the level of calcium

ion to a point which depends on the concentration of the salt in the or- ganic phase and the partition coefficient of the salt between the aqueous

and the organic phase. In general, the lower limit of useful electrode response can be improved

by increasing the molecular weight of the site group and by working with

lower loadings of the salt in the organic phase. Unfortunately, increasing

the molecular weight beyond a certain point may cause precipitation or

gelling in the organic membrane phase. Reducing the concentration of the

salt in the organic phase can also lead to problems associated with higher

membrane resistance and longer time response. A practical electrode is always a result of compromise between these factors. The effect of hydrogen ion interference on the same calcium electrode

is shown in Figure 4. The electrode potential at constant calcium ion concentration is independent of pH until the hydrogen ion activity increases

to a point where kaAn^i^, as defined by Equation (3), becomes appreciable

compared with Aca- The hydrogen ion then contributes to the charge

transport process across the membrane and produces a positive increase

in the electrode potential. With still further increase inAii, a point is reached where the contribution of Ca++ to the charge transport in the

membrane is overwhelmed by hydrogen ion, and the electrode now

responds in a Nernstian manner as a pH electrode.

68 ION-SELECTIVE ELECTRODES

60

40

20

20

40

10'' CaCl2

ELECTRODE

POTENTIAL

(mV)

10 ^CoCI,

8 )0

SOLUTION pH

Figure 4. Effect of.H+ on calcium ion measurements. pH has been varied with incre- ments of HCl and NaOH at the CaClo molarity indicated on each curve. The calcium-phosphate ester salt in the membrane phase is converted

to the free acid form in these acid regions, with the result that, if the elec- trode is then placed in a calcium solution of high pH, there will be a time

interval during which calcium ions displace the hydrogen ions in the membrane. During this period, the electrode potential slowly drifts at a rate which depends on the thickness of the membrane. As a result, the

thin-layer electrode configuration shown in Figure 2 is to be preferred in those applications where it is likely that the electrode will occasionally be

exposed to excessively high concentrations of interfering ions. Sodium ion interference is shown in Figure 5. Because the calcium

electrode does not respond at all to sodium, except at very high ratios of
SOLID-STATE AND LIQUID MEMBRANE ELECTRODES 69

sodium to calcium ion activity, it is experimentally easier to vary calcium

ion activity in the presence of high background levels of sodium chloride.

+100 --

ELECTRODE

POTENTIAL

(mV)

-100

SLOPE 29.5 mV

NaCI

1 M

0.2 M

CALCIUM ACTIVITY (M)

^ 1 h- 10 10 10 10 10 10 10°

Figure 5. Effect of Na+ in calcium ion activity measurements. CaCla varied in the presence

of the indicated background molarity of NaCi.

Again, it can be seen that Equation (3) is obeyed with respect to the major

features of the curves. The curve corresponding to the highest

background level of sodium chloride (l.OM) is displaced from the others

by a small amount. This is caused by a junction potential at the salt bridge

and does not represent sodium ion interference. Selectivity constants cal- culated from Figures 4 and 5, together with constants for other ions, are summarized in Table 1

.

In discussing interferences for liquid membrane electrodes, it is necessary to reemphasize that a selectivity constant is an approximate number.
70 ION-SELECTIVE ELECTRODES
SOLID-STATE AND LIQUID MEMBRANE ELECTRODES J \ Table 1. Liquid membrane systems (continued). Ion measured Exchange site Selectivity constants 0H~ 1.0, I- 1.2 X 10-^

F~ 2.5 X 10-^,

NOs 1.5 X 10"^,

cr 2.2 X

10-"^,

Br" 5.6 X 10-^,

SOI 1.6 X 10"^,

OAc~ 5.1x 10"'* ClOr 32, I" 17, NO^ 4.2, Br" 1.6, OH" 1.0, OAc" 0.32,

HCO3" 0;19, SO4 0.14,

F~ 0.10

OH" 10-^, I" 20,

NOs 0.1,

Br~ 4 X 10-2,

OAc~ 4 X 10-^,

HC05" 4 X 10-3,

F" 10-3, Cl~ 10-3,

SOJ 10-3

and can be used only to estimate orders of magnitude of interferences to be expected in a given application. It cannot be used to make corrections

to electrode readings obtained in solutions in which the level of inter- ference is appreciable. In Figure 6 are shown some experimental values

of obtained with an electrode using a calcium-phosphate ester salt in a mixed alcohol-phosphonate solvent. As can be seen for this typical case, the value of ku^ depends to some extent on solution composition.

If calculation shows that the maximum expected value of an inter- ference term in Equation (3) is small, say less than 2% of the minimum

value of the activity of the sought-for ion, then an electrode can be used

with confidence. For borderline situations, it is best to determine the per- tinent selectivity constants in a solution of ionic composition similar to the samples to be analyzed.

C. Other Cation-Selective Liquid Systems

Charged site groups containing sulfur would be expected to show selectivity toward heavy metal ions which form insoluble sulfides and stable mercapto complexes. The use of mercaptan groups by themselves has not proved fruitful because of their sensitivity to oxidation and the difficulty

of eliminating hydrogen ion interference due to the very weakly acid na-
72 ION-SELECTIVE ELECTRODES

.5-

.4-

.3-

.2 -

.1 -

0 I \ \ \ 1 \ \ \ \ \ h0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 [Ca^l

[Ca^] + [Mg^l

Figure 6. Variation of ky^ with solution composition for an experimental divalent ion

electrode. Data obtained at constant CaCl2+ MgCl2 concentration of 0.01 M.

ture of the site. Site groups of the type R-S-CH2COO-, in which the sulfur and the carboxylate groups are in a position to form a chelate ring with a heavy metal ion, do show good selectivity and are sufficiently stable to form useful electrodes [4].

A calibration curve for a copper electrode based on a thio-acid site is shown in Figure 3. The plateau at low copper levels has the explanation

given previously for the calcium electrode. Selectivity constant data for

this copper electrode, as well as for a lead-selective electrode utilizing the same site group, are given in Table 1. From a practical point of view,

liquid electrodes for heavy metals are now obsolete due to the recent development of solid-state membranes, which in almost all applications

show better selectivities than the liquid systems.

D. Anion-Selective Liquid Systems

By making use of a positively charged site group, it would be expected

that anion-selective electrodes could be fabricated. The most important

class of site groups in this category are complexes of positively charged

transition metal complexes with a bulky organic ligand containing the

orthophenanthroline chelating group. Salts of the type FeL3(N03)2, where

Lisa substituted phenanthroline ligand, function as anion exchangers.

This metal ion complex is non-labile, and the rate of transition metal cat- ion exchange at the membrane interface is too slow relative to the rate of

anion exchange to have any effect on the electrode potential. The positive

charge in sites of this type is largely delocalized because of the aromatic

ring system in the ligand. It would be expected that such low charge den-
solid-state and liquid membrane electrodes 73

sity sites would form more stable complexes with large polarizable anions

than with small "hard" ions, such as fluoride and hydroxide.

Calibration curves for electrodes making use of complex metal sites and selective to nitrate and perchlorate ions are shown in Figure 7. The

only notable difference in these curves compared with the cation-selective electrodes is the change in the sign of the slope. This is to be ex- pected, since it is a negatively charged species which is being transported

across the membrane, and the sign of the logarithmic term in the Nernst

equation changes accordingly. Also, the slope has twice the absolute

value of the divalent cation curves, since we are now dealing with a monovalent ion. Selectivity constants for these electrodes are shown in Table 1. An electrode for fluoroborate ion is also listed in Table 1. This elec- trode resulted from the observation by Carlson [5] that the nitrate elec- trode just described could also be used to measure BF4~ in solutions containing no nitrate ion, provided that the liquid phase of the nitrate elec- trode membrane was first extracted with a solution of NaBF4, thereby

converting the nitrate salt into the fluoroborate form. The internal

reference solution of the nitrate electrode must, of course, be replaced

with one containing a fixed concentration of fluoroborate ion. Another liquid system which has some practical utility uses a high

molecular weight tetraalkyl ammonium salt. A chloride electrode of this type using a dimethyl-distearyl ammonium cation can be used to measure

chloride ion activities in the presence of sulfide and small an cants of bromide and iodide, all of which seriously interfere with the solid-state

chloride electrodes. The properties of this electrode are also listed in Table 1.

VI. Solid-State Membrane Systems

A. General Properties

A few crystalline materials are known which exhibit ionic conductivity

at room temperature. In most cases, only one of the lattice ions is in- volved in the conduction process, usually the lattice ion with the smallest

ionic radius and the smallest charge. Provided that the crystal is mechanically stable, chemically inert in the sample solution, and of low solubility,

it can be used in the form of a thin section as an electrode membrane.

A crystal membrane can be a highly selective device. Conduction in the

crystal phase proceeds by a lattice defect mechanism in which a mobile

ion adjacent to a vacancy defect moves into the vacancy. A vacancy for a particular ion is ideally tailored with respect to size, shape, and charge

distribution to admit only the mobile ion; all other ions are unable to move
74 ION-SELECTIVE ELECTRODES
SOLID-STATE AND LIQUID MEMBRANE ELECTRODES 75

and cannot contribute to the conduction process. With liquid membrane

electrodes, any ion capable of entering the membrane phase is able to move as a site-ion complex, and selectivity therefore must depend entirely on the ion-exchange process at the membrane-sample interface. Solid-state crystal membrane electrodes derive their selectivity by

restricting the movement of all ions except the one to be detected.

Since no foreign ions can enter the crystal phase, the theory of the

solid-state membrane is simple. It always behaves as a Nernstian device.

Interferences can occur, but they arise from chemical reactions at the

crystal surface and are of an entirely different type than in the case of the

liquid membrane electrodes.

B. Rare-Earth Fluoride Membranes

It has recently been observed that electrodes can be made from

fluorides of several of the rare earths, notably lanthanum, which are pure

fluoride ion conducting systems at room temperature [6]. These materials in single crystal form have unusually low volume resistivities which

can be reduced still further by doping the crystal with a divalent cation

such as Eu++.

A calibration curve of a LaFs membrane electrode is shown in Figure 8. Nernstian response is obtained over a range extending from

saturated solutions to IQ-W fluoride ion activity. Below 10 Wfluoride

levels, the calibration curve plateaus in a manner similar to the calibration curves of the liquid membrane electrodes. The reason for the plateau

is the same: the solubility of lanthanum fluoride in the sample solution.

However, the lower limit of detection for the fluoride electrode is much

smaller than one would calculate from the literature values for the solubility product of lanthanum fluoride [7]. Why this should be the case is

still an open question. It may be due to a very slow rate of dissolution of

the membrane in the sample solution, which does not permit equilibrium

to be established in dilute samples during the time involved in making the

measurement. An alternative explanation, and one which seems much

more probable, is that the single crystal material may have a much smaller

equilibrium solubility than the finely divided, freshly precipitated com- pound that has been used for the solubility product determinations.

In addition to being a Nernstian detector of fluoride ions, a lanthanum

fluoride membrane electrode can be used to measure lanthanum ion levels

in solutions which initially contain no fluoride. The electrode potential

is given by the Nernst equation:

JT 2.3RT, . /s = constant =—iog/4p. (4) r

If the sample solution is equilibrated with solid LaFa, then the fluoride
76 ION-SELECTIVE ELECTRODES

Figure 8. Calibration curve for a fluoride ion-selective electrode. level at the electrode surface in a solution containing La^^ is determined

by the solubility product of LaFa, i.e.:

^.s/>(LaF.,) =^La^-F- (5) Substitution of Equation (5) in Equation (4) gives:

E = constant + log A . (6) The slow rate of equilibration of solid single crystal LaF^ with aqueous

solutions necessitates the separate addition of finely divided LaFa to the
SOLID-STATE AND LIQUID MEMBRANE ELECTRODES 77

sample. Although the ability to detect an exotic ion such as lanthanum is of itself of little analytical importance, the fact that a crystal membrane

electrode can be used to detect the other non-mobile ions of the membrane lattice has important practical implications, as will be shown in the

following sections.

C. Systems Based ON Silver Sulfide

Silver sulfide, in common with many other silver salts, is an ionic con- ductor of low resistance in which the silver ions are the mobile species.

The exceedingly low solubility product of Ag2S, its excellent resistance

to oxidizing and reducing agents, and the ease with which it can be

fabricated into dense polycrystalline membranes by conventional pellet

pressing techniques, makes it an ideal material for electrode use. By itself,

it can be used either to detect silver ions or to measure sulfide ion levels by the mechanism of the solubility product equilibrium already discussed

under the fluoride electrode [8]. Because silver sulfide equilibrates very

rapidly with the sample solution, it is not necessary to add additional

solid silver sulfide to the sample. As a silver-ion detector, it is superior to a silver metal electrode, since it is not attacked by strong oxidizing agents,

and it is not sensitive to redox couples in the solution. As a sulfide-sensing

device, it is preferable to the silver metal-silver sulfide electrodes which

have occasionally been used in the past, for the reasons just cited, and

also because the membrane surface is dense and nonporous, resulting in very fast time responses to changes in sample sulfide levels. Calibration curves obtained with silver sulfide membrane electrodes

are Nernstian and are similar to the curves already described for the other

ion-selective electrodes. The dynamic range of the electrode extends from

saturated solutions down to silver and sulfide levels on the order of

lO-^M. The lower limit of detection is far too high to be caused by the

solubility of the membrane [/^sMAf?2s)^ 10"^^] » and reflects instead the

experimental difficulty of preparing extremely dilute solutions of ions

without extensive ionic adsorption on and desorption from the surfaces

of the containing vessels and the electrodes. This problem is identical

to the difficulty faced by an analyst in attempting to obtain accurate pH

readings in very dilute unbuffered solutions.

With solutions of higher levels of silver or sulfide in which extensive

complexation is present, it is quite possible to obtain accurate measure- ments of very low levels of the free ions. Free sulfide ion levels on the

order of lO-'^M, for example, are easily determined in acid hydrogen sul- fide solutions. Similarly, silver ion levels can be followed down to the

10-20^ level during the course of titrations of silver with a number of

complexing and precipitating reagents.
78 ION-SELECTIVE ELECTRODES

D. Mixed AgaS-AgX Systems

Kolthoff reported, many years ago, that chloride and bromide elec- trodes could be made with membranes of fused silver chloride and silver bromide [9]. Both silver chloride and silver bromide are ionic conducting

materials in which silver is the mobile species. Such electrodes sense the

halide ion by a mechanism identical to that of the silver sulfide membrane

in a sulfide solution. Although these electrodes were not affected by

redox couples and were faster in response than the classical silver metal-silver halide electrodes, they were never widely used in chemical

analysis. The principal disadvantages were associated with the rather high

room-temperature resistance of silver chloride, and with the fact that both

materials exhibit large photoelectric potentials requiring that they be used

under conditions of constant illumination, difficult to achieve in the

average laboratory.

We have found that these disadvantages can be eliminated by using

electrode membranes of a silver sulfide matrix in which the appropriate

silver salt is dispersed in a very finely divided form. Since silver halides are much more soluble than silver sulfide, the sulfide can be considered as a chemically inert matrix material through which silver ions are free to move. At the membrane-solution interface, the silver halide equilibrates

with the sample solution, resulting in a silver ion level given by:

Substitution into the Nernst equation for a silver ion conducting membrane gives the result that a mixed sulfide of this type behaves as though

the membrane were a pure halide ion conductor.

The mixed silver sulfide-silver salt approach to membrane fabrication can also be used with silver iodide and silver thiocyanate respectively;

other electrodes can also be visualized. The chief restriction on the silver

salt is that its solubility must be much larger than that of silver sulfide (which will always be the case) and yet be sufficiently small so that the

equilibrium solubility of the silver salt does not give an anion level which

is higher than the expected sample activity.

It is not necessary that the salt AgX be a silver ion conductor, nor is it always necessary that the salt form a mechanically stable pressed pellet

when present in the pure state. Silver iodide, for example, cannot be

formed as a pure Agl pellet and used as an electrode membrane, even

though it is a good silver ion conductor and has a sufficiently low

room-temperature resistivity. Silver iodide undergoes several solid-phase

transformations on heating or on increasing pressure above ambient

values. A pellet prepared by fusion or by pressing slowly reverts to the

(7)
SOLID-STATE AND LIQUID MEMBRANE ELECTRODES 79

Stable room-temperature modification, fracturing in the process. When

prepared as a mixed sulfide pellet, this does not take place, either because

the kinetics of the process are too slow or because the silver iodide has

been converted to the compound Ag;}Sl, which does not exhibit a phase

transition. Calibration curves obtained using the mixed silver sulfide-silver salt membrane electrodes are identical to those which would be expected if the membranes were made from the pure silver salt. Lower limits of sensitivity are determined by the solubility products for the various silver

salts. The properties of a number of examples of this class of electrodes

are summarized in Table 2. Table 2. Solid— stat^^ membrane electrodes.

Ion determined Membrane Principal interferences

F-, La+^^ LaFs 0H~

Cl~ AgCl/Ag2S Br~, I~, S=, NH3, CN~

Br~ AgBr/AggS r, S=, NH3, CN~

I" AgI/Ag2S S^, CN~

SCN- AgSCN/Ag2S Br~, I~, S=, NH3, CN~

S=, Ag+ Ag2S Hg^+

CN~ AgI/Ag2S r, s= Cu^+ CuS/Ag2S Hg^^ Ag+

Pb^+ PbS/Ag2S Hg^^, Ag-^, Cu^+

CdS/AggS

E. Mixed Silver Sulfide-Metal Sulfide Membrane Systems

Silver sulfide'can also be used as a matrix material in conjunction with

a number of metal sulfides to give membranes selective to the metal ion of

the second metal sulfide. As long as the membrane contains sufficient

silver sulfide to provide silver ion conducting pathways through the membrane, it will function as a silver ion detector. The silver ion activity level

at the sample/membrane interface, assuming that the sample contains no

silver ion initially, is determined by the following two equilibria:

/^•l^/is==Ks7>(A.,S) (8)

(9)
80 ION-SELECTIVE ELECTRODES

where MS is the metal sulfide present in a finely dispersed state in the

silver sulfide matrix. Eliminating and solving for Aah gives:

^AK= —\Am\ (10)

which, when substituted into the Nernst equation for a silver ion conducting system, yields:

A = constant H ^^log^M- (11)

The electrode therefore behaves, in solutions containing but not Ag^, as a Nernstian device selective for A^-

There are "several restrictions on the metal sulfide MS which must be

satisfied. The solubility product Kspius) iriust be much larger than that of

Ag2S. If this were not the case, then it would not be possible to have

silver sulfide present on the electrode surface, as the reaction

M++ + Ag2S:^MS + 2Ag+ (12)

would proceed completely to the right. At the same time, the value of

^sp(Ms) rnust be sufficiently small so that the level of M++ in the sample

solution produced from the solubility of MS is small relative to the levels of the ion which are expected in the sample. In addition to solubility

product restrictions, it is also necessary that the sulfides of the membrane

phase equilibrate rapidly with the ions of the sample in order for the elec- trode to have a reasonable time response. Unlike the electrodes discussed

earlier, two solid-phase equilibria must now be established. The resulting

kinetic complications prevent a number of otherwise suitable sulfides

from being used in electrodes.

Among the sulfides which we have found make useful electrodes are CuS, CdS, and PbS. Nernstian calibration curves are obtained in all cases, and the curves extend over a dynamic range from saturated solu- tions at the upper limit to a lower limit which is a strong function of pH.

The pH dependence of the lower limit of sensitivity arises from the in- creased solubility of metal sulfides in acid solution, due to the formation

of HS~ and H2S. The effect of pH on the sensitivity range of a lead elec- trode is shown in Figure 9. Data for the other electrodes are summarized

in Table 2. Data of the type shown in Figure 9 are useful in determining in advance

how dilute a sample may be and still permit a direct electrode measure- ment of the metal ion level. In titration applications involving reladvely

concentrated solutions of the metals in the 10"^ to lO-^'M range, Nernstian response to the free metal ion can be obtained down to very
SOLID-STATE AND LIQUID MEMBRANE ELECTRODES

Figure 9. Effect of pH on a lead-selective electrode. pH varied with HCIO4 and NaOH

at the indicated background level of Pb(C104)2. low levels in the presence of excess reagent [10]. In this case, it is only

necessary that the equilibrium solubility of the metal sulfide in the

presence of the reagent be small compared with the total metal concentration in the solution being titrated. A titration curve obtained with a cadmium electrode showing the variation in free cadmium ion activity with

added EDTA is shown in Figure 10.

F. Interferences at Solid-State Membrane Electrodes

1 have already pointed out that, because of the stringent requirements

regarding size and charge of the mobile ion species in a crystal lattice, in- terference resulting from lattice penetration of the interfering ion is not to be expected with solid-state devices. Such penetration, if it occurred,

would require the existence of stable solid solutions involving the mobile

ion and the interfering ion. Among the compounds we have been

discussing, very few solid solutions of this type are known which will
82 ION-SELECTIVE ELECTRODES

-280-

-340 -

-310-

-430-

-400-

-370-

electrode

potential

(mV)

-460- ml of Na2H2EDTA added

1 2 3 4 5 6 7 8

Figure 10. Titration of Cd++ with EDTA. 100ml of 5X10-W Cd(NO:i)2 adjusted to pH

10 with NH,. Titrated with O.IM Na.H .EDTA. form at room temperature. Glass electrode membranes, however, which

involve a lattice of much higher disorder than the crystalline materials, do

show lattice-penetration interference, and are more properly considered

as a special case of a liquid membrane system in which the sites have zero

mobility.

Nernstian response in a solid-membrane device requires that all the

solid phases of the membrane be in equilibrium with the sample solution. This will not be the case if there are species present in the sample solution

which can react with the components of the membrane. The most com- mon type of reaction, and one which is frequently observed with membranes containing a silver halide, involves reaction with an ion in the sample solution to form a more insoluble silver salt. Thiocyanate ion, for ex- ample, can interfere with bromide ion measurements if the reaction

takes place [II]. This reaction will not proceed to the right unless the

ratio of the thiocyanate ion activity to the bromide ion activity exceeds a value given by the ratio of the solubility products of silver thiocyanate to

SCN- + AgBr(s) ^ AgSCN(s)+ Br" (13)
SOLID-STATE AND LIQUID MEMBRANE ELECTRODES 83

silver bromide. If this ratio is exceeded, then all the silver bromide on the

membrane surface will be converted to silver thiocyanate. The silver ion

activity at the electrode surface will then be determined by the thio- cyanate ion activity, and the electrode will behave as a thiocyanate-sensing device.

An example of the abrupt onset of this type of interference is shown in Figure 1 1. This should be compared with Figure 5, which shows the

gradual increase in the level of interference with increasing activity of the

interfering ion. This latter response is typical of liquid membrane systems.

2.6 . 10-^ M (EXPERIMENTAL)

2.3 X 10-2 ^ (THEORETICAL)

ELECTRODE

POTENTIAL

(mV)

THIOCYANATE CONCENTRATION (M)

Figure IL Effect of SCN" on a bromide electrode. Background solution lO'-W NaBr

with NaSCN added in the amount indicated on the horizontal axis. A more complicated case of interference, resulting in the formation of

a new solid phase, is found with the mixed cupric-silver sulfide membrane

electrode. In samples containing both copper and chloride ions, the reaction: Ag.2S(s)+ Cu++ + 2Cl- = 2AgCl(s)4- CuS(s) (14)

may take place. The condition which must be satisfied, if the silver sulfide on the membrane surface is to be stable, is readily derived from equilibrium calculations, and may be expressed as: Ac^h < (15)
84 ION-SELECTIVE ELECTRODES

where K^g-zs^ ^Agcb ^cus refer to the solubility products of the compounds

indicated by the subscripts. If the sample activity product AcuA'^^ ex- ceeds the value given, then all the silver sulfide at the membrane surface

is converted to silver chloride, accompanied by an abrupt change in electrode function from a Nernstian response to cupric ion to a response

to chloride ion. Fortunately, an electrode is not irreversibly harmed if it is inadvertently

placed in a solution which results in the formation of a new solid phase.

The reactions giving rise to the interferences are all reversible, and the

electrode can be restored to normal operation by exposure to a high concentration of the appropriate ion (bromide in the first example cited), or

to a reagent such as ammonia, which will remove the silver chloride from

a contaminated cupric ion selective electrode. Solid electrodes may also give problems if they are used in samples

containing a species which forms a very stable complex with one of the

component ions of the membrane. An example is the effect of citrate ion on a lanthanum fluoride electrode. Lanthanum ion forms a very stable soluble citrate complex, which has the effect of increasing the solubility

of the membrane in the sample by the reaction:

At equilibrium in a solution originally containing no fluoride, but an activity of citrate, Aau the sample fluoride level in the vicinity of the membrane surface will be given by:

where Kf refers to the formation constant of the lanthanum curate complex. In most cases, the fluoride level given by this expression will be

small compared with the sample fluoride level, and can therefore be

ignored. In dilute fluoride solutions, however, the value of A°p may be apv- preciable compared with the sample fluoride level, and the electrode will give too high a value for the analysis. The effect of the citrate is to in- crease the lower limit of detection of the fluoride electrode by an amount

which increases with the one-fourth power of the sample citrate activity.

Figure 12 shows a set of calibration curves obtained at various citrate background levels. Similar results are obtained in the presence of other

strong complexing agents for lanthanum, such as EDTA.

With a mixed silver iodide-silver sulfide membrane in contact with a cyanide solution, a similar reaction occurs:

LaF3(s) + Cit'^- ^ LaCit" + 3 F". (16)

A°^^4[KfK^,^,AcitV" (17)

Agl(s) + 2CN- - Ag(CN).r + I-. (18)

In this case, however, the reaction proceeds virtually to completion at equilibrium with the consumption of silver iodide from the membrane and

86 ION-SELECTIVE ELECTRODES

the production of iodide ions. The iodide and cyanide ions interdiffuse

between the eroding electrode surface and the sample solution. If an ap- propriate diffusion barrier is placed on the membrane surface, then a steady state is quickly established in which the cyanide level at the solid membrane surface is virtually zero, while the iodide level is very nearly

one-half the sample cyanide ion concentration. The silver ion activity at the membrane surface is fixed by the iodide level via the solubility

product of silver iodide, and the electrode potential as a result depends in an almost Nernstian manner on the sample cyanide ion concentration.

We have found that the porous silver sulfide matrix left behind as the

silver iodide is consumed provides an almost ideal diffusion barrier. The

flux of iodide and cyanide ions is kept sufficiently low so that electrode

lives of several months of continuous operation are possible. At the same

time, the porous silver sulfide layer never becomes thick enough to adversely affect the electrode time response. The outermost silver sulfide layers are continuously sloughing off at a rate which keeps the effective

diffusion barrier thickness a constant. A pseudo-Nernstian electrode of this type is not as convenient a device

as the other solid-state electrodes which have been discussed, because of

its limited life. The precision with which analyses can be made, however,

especially in dilute solutions, is as good as that obtained with other elec- trodes, and the cyanide electrode finds wide use in such applications as

plating solution analysis and water pollution monitoring.

VII. Future Developments

In this presentation, I have discussed only two approaches to the construction of ion-selective devices — solid-state and liquid membrane

electrodes. Glass and heterogeneous membranes are two other ap- proaches which have received attention by other workers in recent years, and undoubtedly new and presently unsuspected materials will be un- covered in the future. I would like to close by giving my own, highly per- sonal, estimation of what will be forthcoming during the next few years in each of these areas. Glass membranes were the first ion-selective devices, and there is a his- tory of at least thirty years of active research in the field of new and useful

glass compositions for electrode use [12]. A large number of pH-sensitive compositions have been discovered, as well as several highly useful sodium ion-selective glasses. Unfortunately, the range of site types that can be incorporated in a silicate glass lattice is relatively small, due principally to the severe restrictions imposed by the high melting point of the

glass. In view of the large amount of work that has already been devoted

to this area and the limited range of available sites, I feel that there will be

little forthcoming, at least as far as additions to the list of ions which can
SOLID-STATE AND LIQUID MEMBRANE ELECTRODES 87

be detected. Undoubtedly though, new and better glass compositions,

from the standpoint of chemical durability, strength, and absence of drift, will be discovered. Nonsilicate, organic glasses present an interesting al- ternative to silicate glasses, chiefly because of the much larger spectrum

of sites that can be used, and this area deserves investigation.

In terms of the number of different ions that can be detected, the or- ganic liquid membranes offer the most versatile approach to ion selectivity. Virtually any ion, mono- or polyvalent, cation or anion, can be deter- mined with these systems. This versatility, however, is achieved at the ex- pense of selectivity, which rarely reaches the high order of selectivity

found in solid-state systems. Still, however, the selectivities are adequate

for many analytical applications, and certainly many new electrodes of

this type will become available in the near future. The principal problem

in the liquid membrane field is, at present, the lack of data on complex ion

stabilities in low dielectric constant solvents and on the mobilities of the

various species which are formed in these solvents. These data are needed both for the intelligent selection of appropriate site groups for a given application and also for devising realistic models for the transport

process and the testing of the theoretical equations which the models suggest.

Solid-state membranes made from crystalline materials have only

recently received serious consideration. Development of new electrodes

of this type will depend on finding new classes of ionically conducting

materials. At the present time, only the rare-earth fluorides and the vari- ous silver salts show sufficient ionic mobility at room temperature to be

useful as membrane materials, most crystals being good insulators. Unfortunately, our understanding of ionic conduction in the solid state and

its relationship to crystal structure is very limited, making it impossible to predict if a known crystal will show useful electrode properties. The

number of untried materials is vast, and the experimental process of

evaluation is slow. Any large-scale breakthrough in this area will have to await a better theoretical understanding of solid-state ionic conduction, so

that the intelligent screening of all the known insoluble crystalline materials can be made. It is probably safe to say that only small univalent ions can have a significant mobility in a crystal lattice at room temperature.

Solid-state electrodes sensitive to polyvalent ions are unlikely to be

found, and any advances in the search for solid-state sulfate or phosphate

electrodes probably will be made via the establishment of a solubility

equilibrium with a measurable monovalent ion. Heterogeneous membrane electrodes in which a finely divided solid material is embedded in an inert, nonconducting matrix are difficult to

classify. Membranes made from ionically conducting solids, such as the

silver halides [13], are identical to the solid-state electrodes in both

mechanism and electrode response to the mobile ion. For these mem-
88 ION-SELECTIVE ELECTRODES

branes, the comments of the last paragraph apply. In addition, however,

membranes have been described in which the suspended solid is a non- conductor, such as electrodes made with barium sulfate for which sulfate ion response has been reported [14]. Membranes made from nonconductive materials must operate by a surface conduction process on the inter- face between the dispersed solid and the inert matrix. Virtually nothing is known about this surface conduction process, and it is impossible to predict what further study will uncover. The surface conduction approach is an interesting one, and suggests also that ion diffusion in grain boundaries

in other solid-state systems should be investigated.

In summary, I would point out that the past several years have seen the

development of over twenty ion-selective electrodes. This represents the

fruits of largely Edisonian research, and I would think that the rate of new

electrode introduction will be much slower in the near future. Further ad- vances must await a better theoretical understanding of the subject. This

temporary hiatus can be used to good advantage by analytical chemists,

however, since there remains much to be done in the application of the

presently existing electrodes. These electrodes are currently being used

in only a small fraction of the applications for which they have a potential use, both in research and in industry. The recent exponential increase in publication of electrode applications reflects this situation, and a still further increase is to be expected.

VIII. References

[ I] RossJ.W., Science 156,3780(1967).

[ 2] Eisenman, G., Anal. Chem. 40, 3 1 0 (1 968).

I 3J Kielland,J.,.l. Amer. Chem. Soc. 59, 1675 (1937).

|4j Ross, J. W. and Frant, M. S., Liquid Ion Exchange Membrane Electrodes. Paper

presented at Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, March 1966.

I 5] Carlson, R. M. and Paul,,I. L., Anal. Chem.40, 1292 (1968).

[6] Frant, M. S. and Ross, J. W., Science 154, 3756, (1966).

I 7] Lingane,.!..!., Anal. Chem. 39,881 (1967).

I 8] Frant, M. S. and Ross, J. W., A New Electrode for Sulfide Activity. Paper presented

at the Eastern Analytical Symposium, New York, November 1966. Rechnitz, G.

A. and Hesu,T. M., Anal. Chem.40, 1054(1968).

[9J Kolthoff, I. M. and Sanders, H. L., J. Amer. Chem. Soc. 59, 416 (1937).

[10] Ross, J.W. and Frant, M. S. Use of New Ion-Selective Membrane Electrodes for Titrations of Copper, Lead and Cadmium Paper presented at Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, March, 1969.

| li] Ross, .1. W. and Frant, M. S., The Mechanism of Interference at Solid-State Ion-Selective Electrodes. Paper presented at Pittsburgh Conference on Analytical

Chemistry and Applied Spectroscopy, March, 1968.

I I2J Glass Electrodes for Hydrogen and Other Cations, G. Eisenman, Ed., Marcel Dekker, Inc.. New York, 1967.

I 13| Pungor. E.,Havas,.I., and Toth,K.,Z. Chem. 1,9(1965).

I 14| Rechnitz, G. A., Lin,Z. F., and Zamochnick, S. B., Anal. Lett. 1,29(1967).
CHAPTER 3

HETEROGENEOUS MEMBRANE ELECTRODES

Arthur K. Covington

Department ofPhysical Chemistry

School of Chemistry

University of Newcastle

Newcastle upon Tyne, England

I. Introduction

The subject of the development of electrical potentials across membranes has received much attention over the past seventy years, principally because of its importance in biological processes. The subject has

been extensively reviewed recently from different standpoints [1-3] and

it is not the intention to provide an extensive historical review here. It is important to realize, however, that a wide range of membrane types is possible, from material with pores of several times ionic dimensions, impeding the flow of solutions, to membranes in which equilibria are separately developed on two surfaces and electronic or ionic conduction

processes in the solid are responsible for linking these. In between these

extremes, the terms semipermeable and permselective are used to describe membrane behavior; the unqualified general use of the word

membrane must not, however, be construed as implying any connotation

as to the mechanism of its operation. As will be emphasized later, it is dangerous to make inferences about the operation of one particular type

of membrane and the mechanism of the setting up of a potential difference across it, from the properties of another type.

Recent developments in ion-selective electrodes culminating in their

commercial availability, can be directly traced to the work of Marshall on

zeolite and clay membranes, of Tendeloo on natural heavy spar (BaS04)

and fluorite (CaF2) membranes, and of Michaelis and of Sollner on col- lodion membranes, to mention only a few of the principal workers in a

vast literature.

II. The Development of Heterogeneous Membrane Electrodes

A useful distinction can be made between homogeneous and

heterogeneous membranes. In the latter, which are our concern here, an

inert binder material is used to form the membrane and give it the required

mechanical properties. The new solid-state membrane electrodes, part of

the subject of Chapter 2 [4] , come into the first category, and perhaps are

to be regarded as a more perfect form of the latter. However, it may not always be feasible to obtain a material in the requisite single crystal or 89
90 ION-SELECTIVE ELECTRODES

fused form, and it may be possible to control more easily the properties of

the dispersed material. The two types are therefore to be regarded essentially as complementary.

Although the role of the binder material is simply to provide an inert matrix in which the material of interest is embedded, its properties are obviously important. It must first be chemically inert, and provide the cor- rect adhesion properties with the particles. Paraffin wax and collodion

have already been mentioned as binder materials but polyvinyl chloride

(PVC), polystyrene, polyethylene and most important, silicone rubber

have been used. The latter has ideal hydrophobic qualities and its flexibili- ty and resistance to cracking and to swelling in aqueous solution make it the most valuable material yet found. This fact, alone, has led to the commercial developments.

It is worth distinguishing between the types of material that have been

dispersed in an inert matrix and the properties and uses of the electrodes

thus formed:

A. Ion-Exchange Resins

Wyllie and Patnode [5] were the first workers to embed ion exchange

resins in an inert binder to achieve robust membranes. Since then, the

technique has received much attention. Recent work includes that of

Bose [6], Basu [7], Hale and McCauley [8], and Joshi and Su- ryanarayana [9]. Parsons [10] showed that Amberlite IR 120 dispersed

in polystyrene and soaked in sodium chloride solution gave a sodium ion

response. However, the most extensive studies have been those of Pungor and his collaborators [11-13] who have prepared ion-exchange resin

electrodes based on silicone rubber which show response to sulfate,

chloride, hydroxide, hydrogen, potassium, zinc and nickel. "Complexonite" (ion-exchange resin containing imino diacetic acid groups) membranes were also investigated in the case of zinc, nickel and aluminum. It was concluded [13] that all these membranes are selective to ion valence

type only and not to individual ions. Some interesting experiments were

carried out with silver, platinum or mercury between two rubber membranes which showed that diffusion potential effects could thereby be

reduced.

B. Precipitate Type

The materials used include sparingly soluble metal salts and a few metal

chelates. Table 1 gives a summary of the principal developments in the

field. The literature tends to be full of contradictory conclusions, and this

is indicative of factors which are not known to, or fully under the control

of, the investigators.
HETEROGENEOUS MEMBRANE ELECTRODES 9]

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U o IICC Q.

to CO 2 I

-a

fate

Odii sul odi( 5

lum o

Silv Bari Silv < CL

2i 6

eg

* 8
92 ION-SELECTIVE ELECTRODES

Ml o 4; c

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5 e

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0) •5 ^

5 ^

I"

^3 c o

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3 B

(N Q " ~ O Z S Z

o

a.

1 igS S U. O

hs O 3 c zoos E- -3

0) lO
HETEROGENEOUS MEMBRANE ELECTRODES 93

Tendeloo and Krips [14-16] studied paraffin membranes incorporating

calcium oxalate, a non-ionic detergent and gauze on which the membrane

was supported. Some degree of calcium ion response was claimed, and

the calcium stearate electrode [17] was investigated. Their conclusions

about the specificity of these electrodes were challenged by Cloos and

Fripiat [18] who found the calcium oxalate-paraffm electrode to be

porous and non-specific. Shatkay confirmed this [19] and found a pure

paraffin electrode to give the same response as the calcium oxalate-paraffm electrode. He found that gauze was necessary to make the membrane

conducting and therefore played an important role in the mechanism. The

conductance could also be increased by greatly increasing the proportion

of calcium oxalate in the binder. Pungor [11] has suggested that Tendeloo's results were vitiated by the small amount of active material used.

Pungor, Toth, and Havas [11] maintain, however, that paraffin and sil- icone rubber based electrodes have both proved to be perfectly permselective. Buchanan and Seago [20] considered that microcracks were

responsible for the functioning of paraffin membrane electrodes. Fischer

and Babcock [21], who also dispensed with the gauze in the preparation

of barium sulfate-paraffin membranes, concluded that their membranes

were not perfectly permselective to either cations or anions. Even so, they considered that such electrodes could be useful indicators for potentiometric titrations involving barium or sulfate ions. Radiochemical stu- dies showed that barium ions were immobile but that sodium or chloride

ions could migrate through the membrane in about 15 minutes.

Hirsch-Ayalon [22] prepared barium sulfate cellophane membranes by

placing barium hydroxide on one side of the membrane and sulfuric acid on the other. Geyer and Syring [23] investigated the properties of some hydrated

oxides dispersed in paraffin or polyethylene and their suitability as elec- trodes for potentiometric titrations. Transition metal salts such as phosphates of cobalt, nickel, copper and manganese in paraffin, collodion

and silicone rubber have variously been studied by Morazzani-Pelletier

and Baffler [24], and by Buchanan and Seago [20]. These latter workers

found that the crystalline form, the degree of hydration and the anion of

the active material had little or no effect on the membrane electrode

response or selectivity. All the electrodes proved to be non-specific,

responding to the total ion content whether this was divalent or univalent

ions. Results obtained using metal chelates as active material are discrepant.

Geyer and Syring [23] were unable to repeat the work of Pungor and

Toth [28] with nickel-responsive electrodes formed using nickel

dimethylglyoxime (NiDMG), but the latter workers claimed theoretical

response for only 6% of the electrodes prepared and only 30% showed

any response at all. Buchanan and Seago [20] also found no response
94 ION-SELECTIVE ELECTRODES

with NiDMG or with nickel acetylacetonate dihydrate. Geyer and Syring

[23] report successful potentiometric titration experiments with membranes containing potassium hexafluorosilicate, silver ferrocyanide and

lead tungstate.

The first studies of Pungor and his collaborators [26] were with silver iodide paraffin membranes, but since then he has exclusively used sil- icone-rubber based membranes containing, for example, silver halides,

sulfide and barium sulfate. Macdonald and Toth [27] have studied the

possibility of obtaining selective fluoride response from lanthanum, thori- um or calcium fluoride impregnated silicone rubber electrodes. More

details of the work mentioned in this paragraph will be given in Section C.

A study which may indicate a useful line for further research is that of

Shatkay [19] with solid polymeric membranes of PVC containing tributyl

phosphate and 2-thenoyltrifluoracetone (TTA). The latter is a chelating

agent and perhaps surprisingly it does not seem that TTA is incorporated

as its calcium enolate form. Shatkay found that the TTA polymeric

membrane and the Orion liquid ion-exchanger electrode gave comparable

results. C. Other Materials

It is appropriate to mention here silicone-rubber based electrodes containing graphite, carbides, borides and silicides which have recently

received attention as possible improved-form electrodes for redox potentiometric titrations and voltammetry. The graphite impregnated electrode

has been introduced by Pungor, Szepesvary and Havas [29] for voltammetry where it appears to offer advantages. It is commercially available.

Some applications have been discussed by Farsang [30]. Weser and

Pungor [31] have investigated the suitability of a very large number of car- bides, borides and silicides as redox electrodes for the ferrocyanide-ferricyanide system as judged by the potential compared with a graphite or platinum electrode in the same solution and the response time. They point out that nearly ai! the suitable materials possess simple face-centered

cubic crystal structures but the significance of this observation is not known.

III. Properties of the Most Useful Electrode Systems

A. Preparation

The properties of the active material are obviously of critical importance to the functioning of the membrane electrode. The most important properties appear to be grain size, crystalline form, conditions of

precipitation (which reagent in excess) and solubility product. Macdonald
HETEROGENEOUS MEMBRANE ELECTRODES 95

and Toth [27] approached this problem from the viewpoint that a good

precipitate for gravimetric analysis will be a good active material for a membrane electrode. For barium sulfate and silver chloride electrodes,

the precipitates were prepared with an excess of anion [32], For

lanthanum fluoride, the opposite is necessary [27]. For silver iodide, it does not appear to matter. The optimum grain size is in the region

1-15 /Ltm. Precipitation in the presence of p-ethoxychrysoidine retards

secondary nucleation. Optimum proportion of active material to binder is about 50 wt %; the essential feature to the successful functioning of the

electrode being that the particles of the active material should be in contact in order to achieve conduction through the membrane. Whether this conduction is achieved through the particles or over their surface is a moot point.

Full details of the membrane preparation have not been published but

the following may be typical [33]. The active material is dispersed in polysiloxane in a laboratory mixer. Homogenization is carried out in a

small roller mill and, at this stage, the cross-linking agent (silane derivative) and catalyst are added. The degree of cross linking determines how

well the particles remain embedded in the surface of the final membrane,

which is now formed by calendering. The cured membrane is removed

from the roller, and discs are cut from it. Discs about 0.3-0.5 mm thick are secured into the ends of glass tubes using silicone rubber adhesive.

Buchanan and Seago [20] used simply a room temperature vulcanized sil- icone rubber (General Electric, "Clear Seal"), which was mixed with finely powdered active material and pressed between a heavy polyethylene

plate and a PVC sheet to give a 0.5 mm thick sheet. Subsequent conditioning of the membrane is important [20] and a few

hours' soaking in an appropriate solution is suggested. An internal

reference electrode is necessary, and the solution must contain one of the

ions of the active material. Thus, for the iodide electrode, a conventional

silver iodide electrode in potassium iodide solution is used or a silver wire

in silver nitrate solution for the sulfide electrode.

B. Silver Halide Electrodes

A few results obtained with the chloride electrode were presented by

Pungor, Havas and Toth [12] and with the iodide electrode by Pungor,

Toth and Havas [11]. More detailed results with the bromide and

chloride electrodes were given by Havas, Papp and Pungor [32]. Independent appraisal of the commercial forms of these electrodes has been

carried out by Rechnitz, Kresz and Zamochnick [34] (iodide) and by

Rechnitz and Kresz [35] (chloride and bromide). Published information on the commercial forms is summarized in Table 2 and some applications

given in Table 3. Pungor [36] has presented a general review of his work
96 ION-SELECTIVE ELECTRODES

Electrode

Iodide Selective

Bromide

Selective

Chloride

Selective

Sulfide Selective

Table 2. Characteristics of commercially available heterogeneous membrane (Pungor-type) electrodes.^ Suggested Type no. 0P-I_711

OP-Br-711

Measurement plon range

OP-S-711

7pl

5 pAg

5 pCN (pH

1 - 6 pBr

1 - 5 pCl

Selectivity Concentration not to exceed: 10" ^ M KCl

10-1 MKBr

1 M K2SO4

1 M KNO3 2<pH<12

Concentration not to exceed: 10" ^ M KCl

1 M K2SO4

1 M KNO3 2<pH<12

Concentration not to exceed: 1 M K2SO4

1 M KNO3 2<pH<12

No interference from: r, Br", Cr, NOT,

SOf", POf- or from CN"

if ten times less than S'^~" concentration

Temperature

range

5 - 50 °C 1-2 hours in

5 - 50 °C 1-2 hours in

5 - 50 °C

5 - 50 °C

10-3

1 — 2 hours in 10-1 - 10-3 M

1 — 2 hours in 10-1 - 10-3 M ^gf^Qg

Carbon

Voltammetric Carbon

Potentiometric

OP-VM-711

OP-C-711

5 pOx(Red)

4 pOx(Red) 90 °C 1 hour in distilled water

'Information derived from the brochures of Radelkis Electrochemical Instruments, Budapest D, Hungary.

Table 3. Some applications of Pungor-type membrane electrodes. Chloride Electrode Determination of organic bases through their hydrochlorides;

Chloride in urine and horse blood serum.

Iodide Electrode Titration of mixed halides;

Iodide content of Hungarian mineral waters;

Sulfur dioxide determination by iodine— iodide;

Cyanide content of amygdalin by hydrolysis;

Cyanide content of sewage, brandies, peach

leaves;

Anodic corrosion of silver.

Sulfide Electrode Titration of mixed halides;

Sulfide content of waste liquor of sulfate paper pulp production;

Sulfide content of brine liquors used for dehairing leather.
HETEROGENEOUS MEMBRANE ELECTRODES 97

up to June 1967. In this paper, results are presented graphically for the

calibration of the silver halide electrodes. Linear response is shown

between pX 1-4 for chloride and bromide, and pX 1-5 for iodide with a

slope of about 56 mV/pX (concentration). Rechnitz et al. [34,35] obtained the following results from the commercial forms: 56 ±3 mV/pI

(iodide, pi 1-6); 53.6 mV/pBr (bromide, pBr 1-3.5); 55 mV/pCl (chloride,

pCl 1-3). The electrodes also respond to silver ion (57 mV/pAg;pAg 1-4; chloride electrode [36]). Overall reproducibility is about 1 mV. The

only effect of cations on the calibration curve is through the different mean ionic activity coefficients. This was shown by Rechnitz, Kresz and

Zamochnick [34] for the iodide electrode in the presence of potassium,

barium and cerium iodides. As expected, the deviations at low pi are

greatest for the cerium salt. The lower limit of detection of the electrodes for halide ions will depend

upon the solubility product of the precipitate. This problem is akin to that of the excessive solubility of material from electrodes of the second kind

[37]. An additional potential term (RTIF) In (1 + SIC) will arise where

S is the solubility of the silver halide in the halide solution of concentration, C. When 5 = C/10, the additional term will be 2.4 mV, which is about detectable as a deviation from a linear calibration curve. Since the

solubility product of the silver halide (Ksp) is given approximately by

then solving the quadratic gives C-(9.1 Ksp)"^. Thus C=3x IQ-^Mfor

silver iodide, 2.7 x lO ^M for silver bromide and 3.8 x lO-^M for silver chloride. This method is simpler and hence preferable to that of Pungor,

Toth and Havas [38; see also 32,36].

Havas, Papp and Pungor [32] have studied the effect of another halide

solution on the chloride and bromide electrodes, and Rechnitz et al. [34,35] have studied all three electrodes. Rechnitz [39] expresses the

selectivity for one ion over another in terms of Equation (1)

written for chloride and bromide ions in terms of their activities, where

/Cfir, ci is the selectivity constant. This has the form of the original equation of Nicolsky based on his ion-exchange theory of the glass electrode

[40], but it is sometimes called the simplified Eisenman equation [41]. If measurements are made in two solutions each containing one of the

cations only, at say O.IM, then

Kst>--S(S + C)

E = constant 4- (RTlF) In (^Br + A^Br.ci^ci) (1)

(2)

hence the selectivity constant can be determined as «ci/«Br 1. From
98 ION-SELECTIVE ELECTRODES

this equation, Rechnitz's definition [34,39] of selectivity arises as the

ratio of the chloride ion concentration to the bromide ion concentration to yield the same emf under otherwise identical conditions. The above is also the method used by Eisenman [41] to determine selectivity constants for aluminosilicate glasses showing mixed sodium-hydrogen ion

response. The same definition can, of course, be used for anion-selective

electrodes. In this way, Rechnitz et al. [34,35] have derived selectivity ratios for the Pungor type silver halide electrodes as shown in Table 4. Pungor et al. [32,36,42] have given a generalized equation, which for a bromide electrode in the presence of several anions, /, (including bromide) takes the form:

^= constant -h {RTIF) In a^,^K^,j f-^) (3) We have retained the same example as before for clarity. As for the glass

electrode, the selectivity constant is interpreted in terms of the equilibrium constant for the exchange process:

AgBr (s) + CI- AgCl (s) + Br"

for which K^r,c\ = Ksp {AgBr)lKsp (AgCl) in this special case. But _AciaBv

^Br, CI — J

y"*) ^Br^Cl

writing /4ci, A^j. for the ionic activities in the solid. If £ = constant + (RT/F) \n^' (5) ^Br

represents the potential arising across the outer surface of the membrane

by virtue of the equality of electrochemical potentials, then substitution

may be made for/^gr. However, following Nicolsky's treatment [40] and

writing concentrations for activities in the solid, then Cc\=Co — CBr,

where Co is the total anion concentration (the concentration of exchangeable sites on the glass surface in Nicolsky's theory). Accordingly,

and by substituting Equation (6) into Equation (5), there results RT RT £= constant + —In (aBr + ^Br, ci«ci) In Co (7)
HETEROGENEOUS MEMBRANE ELECTRODES 99

which is identical with Equation (1) except for the last term which can be

included in the constant. Equation (7), is also identical with Equation

(3) written for bromide and chloride ions. Thus Pungor's Equation (3) and

the Nicolsky-Eisenman Equation (1) are essentially the same, and the

selectivity constant K has the same interpretation.

There appears to be some confusion whether the selectivity constant is to be written in terms of the equilibrium constant for the exchange

process or its reciprocal. Nicolsky [40] originally used the latter. However, it is clear that Kij = llKji, and Equations (1) and (3) have symmetrically related forms.

In Table 4, we compare the selectivity constants as defined above (the

first mentioned ion is that of the precipitate embedded in the electrode

membrane) obtained by Rechnitz and by Pungor and their respective

coworkers. Pungor et al. [42] obtained their selectivity constants from

the ratio of the concentration of the interfering ion to that of the ion to which the electrode is primarily responsive evaluated at the break in the

calibration curve. Differences are no doubt a result of the different experimental approaches.. It may be mentioned that Bishop and Dhaneshwar

[43] have carried out similar experimental studies of the behavior of

conventional silver halide electrodes in mixed halide solutions with

somewhat analogous results.

Table 4. Selectivity constants^.

Pungor et al. Rechnitiz et al. Calc.^ [36 ,42]^ [34, 35]

Bromide Electrode Kgr, ci 4.9 x 10"^ 1.5 x IQ-^ 1.0 x lO'^

Iodide Electrode Kj, Br 1-3 x lO""^ 2 x 10"^ 4.8 x lO'^

^Values are for the equilibrium constant of the exchange process

AgX (in electrode) + Y~ AgY (contaminating + X~

the electrode)

^ From solubility product ratio.

*^ Determined from the break in the emf curve; values (25 °C) are reciprocals of selectivity constants given in [36, 421 ^Determined from measurements in pure potassium halides at 0.1 M

and 30 °C; values here are the reciprocals of the selectivity

ratios given in [34, 35] .
100 ION-SELECTIVE ELECTRODES

The effect of anions which complex with silver, e.g., CN~ and

SzO^ has been studied [42]. All three electrodes respond to cyanide

(Fig. 1). Rechnitz et al. [34] studied interferences by ferrocyanide,

phosphate, perchlorate and sulfate on the iodide electrode; the effect diminishing in the order given. They pointed out that interferences were

not simply a function of the solubilities of the respective silver salts. However, this conclusion is doubtful and may be a result of the method of

determining the selectivity ratios, through Equation (1). The response times of the electrodes have been studied by Rechnitz et

al. [34,35] who find that the half times for response to a twofold change

in anion concentration ranged from 8 seconds for the silver iodide elec- trode to 20 seconds for the silver chloride electrode. The response time of

the iodide electrode in cyanide solutions is similar [42] . The successive

J12\ I \ L

3 4 5

-log CN

Figure \. Response of silver iodide electrode to cyanide ion (after [42]); Reference elec- trode: KN03||KCI(sat)|Hg2Cl2; Hg.
HETEROGENEOUS MEMBRANE ELECTRODES 101

titration of chloride, bromide and iodide with the silver iodide electrode

has been described [44] ; the sulfide electrode is even more suitable for

this purpose.

C. Sulfate and Phosphate Electrodes

The barium sulfate impregnated electrode was one of the first studied

by Pungor and his collaborators [11-13]. The response, to changes in sulfate concentration in the range 10-^ - IQ-^M, was encouraging (24-29

mV/pS04). However, some difficulties must be present, for this electrode

has not yet appeared commercially, although Rechnitz, Lin and

Zamochnick [45] have carried out appraisal studies of a prototype form.

They found an approximately Nernstian response (31 mV/pS04) at concentrations of potassium sulfate above lO^W. Chloride ions interfere

when present above \0-^M.

A phosphate electrode consisting of bismuth phosphate as the active

material [45] was similarly studied. The particular electrode used showed

poor stability (drifting 1 mV/10 min even after extensive soaking). Even

so, the titration curve of phosphoric acid with sodium hydroxide showed

two inflections corresponding to the first and second dissociations of

phosphoric acid. It seems likely that these two prototype electrodes were

not representative.

D. Sulfide Electrode

The behavior of the sulfide electrode which consists of silver sulfide impregnated silicone rubber has been described by Pungor, Schmidt and

Toth [46] . This electrode is probably one of the most important of the new ion-selective electrodes as the conventional silver-silver sulfide elec- trode does not appear to be well characterized [47] although at least one

firm includes it in their catalogue of reference electrodes.

The sulfide membrane electrode gave a linear calibration curve (Fig. 2)

in 0.5-10~W sodium sulfide solutions containing 10~W sodium hydroxide. It also showed a linear response to silver ion in the range of pAg 1-5. Studies with 0. IM sodium sulfide solufions at different pH yielded a

linear pH versus pS plot (Fig. 3) from which pK2 for

HS-+H2O ^ Sf + H30+

was evaluated to be 12.65 (compared with the accepted value of 12.92).

From the potentiometric titration of sodium sulfide with silver nitrate, the

solubility product of silver sulfide was esUmated at 10-43 5 Hseu and

Rechnitz [48], using the commercial solid-state electrode, found 1.5 x

10-^1 for the solubility product. A detailed comparison of Hseu and
102 ION-SELECTIVE ELECTRODES

Rechnitz's appraisal [48] of the solid-state electrode and the above mentioned study of the heterogeneous membrane electrode is not possible

from the results presented. However, Hseu and Rechnitz found a linear

calibration curve down to pS = 7 for the solid-state electrode, whereas

Pungor et al. [46] found that deviations commenced at pS = 4. This

could be a liquid junction potential effect, since Hseu and Rechnitz added

sodium nitrate to their sulfide solutions. A direct comparison of the two

electrodes would be valuable, as indeed would be comparative studies of

the solid-state halide electrodes with the corresponding heterogeneous

membrane halide electrodes. E. Fluoride Electrode

No commercial heterogeneous membrane fluoride selective electrode

has yet appeared, but Macdonald and Toth [27] have published some

developmental studies aimed in this direction which were commenced before the sohd-state lanthanum fluoride electrode became available commercially.
HETEROGENEOUS MEMBRANE ELECTRODES 103

pH

7 8 9 lO II 12 13 1 \ I

\ \

\—r~i

I

I

• /

I /

pS

- 5 - 6 / — 1

Figure 3. Relation between pH and sulfide concentration in sodium sulfide solutions (stoichiometric sulfide concentration 0.1 A/) (after [46]); Reference electrode: KNO.illO.lM KCllAgCl; Ag.

They selected thorium, calcium and the rare earth fluorides for study as being suitably insoluble. Detailed investigation of precipitation

procedures was necessary since normal precipitates of these fluorides

tend to be gelatinous. Electrodes prepared from lanthanum fluoride

precipitated from sodium fluoride with a 30% excess of lanthanum acetate

in the presence of p-ethoxychrysoidine gave reproducible and theoretical

response over the range pF 2-4. Response times were rapid, but production success was unpredictable.

Calcium fluoride precipitates prepared under conditions of excess

anion showed selective response to fluoride with 80% of the theoretical

response over the range pF 2-4. Incorporating carbon with the precipitate

extended the response to pF 5 and improved the response time. However,
104 ION-SELECTIVE ELECTRODES

these electrodes tended to lose their sensitivity after a few weeks and also

tended to swell, probably because calcium fluoride is hygroscopic.

The most suitable material appeared to be lanthanum fluoride but in comparison with the solid-state electrode, which can be used in the range

pF 1-6, the performance of heterogeneous fluoride electrodes was disappointing. Recent studies are more promising [49]

.

rv. Theuretical Considerations

Pungor and his coworkers [11-12] have used the device of embedding

a silver foil between two silicone rubber discs, from which electrodes are made, to show that there is no material transport through the membrane.

In 1937, Kolthoff and Sanders [50] investigated the use of cast silver chloride discs in the cell: Ag; AgCl I KCl I AgCl disc | AgNOs || KNO3I | KCl(sat) | Hg2Cl2; Hg

showing that this was equivalent to the cells Ag; AgCl I KCl I AgCl; Ag . . . . Ag; AgCl | KCl(sat) | Hg.CU; Hg.

They further showed that the potential of the first cell was not sensitive to the addition of oxidizing agents such as potassium permanganate, but the same was not true of the cell combination using conventional silver-silver chloride electrodes. This is the principal advantage claimed for both

solid-state and heterogeneous membrane halide electrodes over conventional electrodes. The question then arises, is the functioning of the silver chloride membrane in either homogeneous or heterogeneous form any dif- ferent from that of two conventional electrodes in opposition except that the silver wire is absent and conduction is provided within the silver chloride? One difference could lie in whether the silver halide coating on the

electrode of the second kind is coherent or cracked and porous [51]. For

adequate functioning of an electrode of the second kind, there need only

be a saturated solution of the salt in contact with the metal.

Pungor et al. [36,42] discussed the mechanism of the formation of the

membrane potential in terms of an exchange equilibrium and the distribu- tion of ions across the inner and outer surfaces of the membrane as in Nicolsky's theory of the glass electrode (see Section III-B). Experiments

with radiotracer iodide showed that the exchange was rapid. The silicone

rubber matrix swells very slightly in water (0.1%), and this fact was in- terpreted in terms of the formation of a swollen layer on the membrane

surface analogous to the silicic acid layer on the surface of the glass elec- trode. Such analogies are rather dangerous. That the correct form of

Nernst-type equation, which expresses the experimental behavior of
HETEROGENEOUS MEMBRANE ELECTRODES 105

membrane electrodes, can be derived by purely thermodynamic means is no guarantee that any of the assumptions made about the processes

responsible are valid. Different models may produce the same form of the

equation. Further, the mechanisms involved with solid-state membranes,

glass electrodes and ion exchange resin membranes may be different,

while formally leading to the same thermodynamic equations.

Buck [52] has discussed the theory of solid-state membrane electrodes

from the point of view of interface potentials and diffusion potentials in a way similar to what Eisenman has done for the glass electrode [53]. Dif- fusion potentials are zero under zero current conditions for pure crystalline membranes. Buck [52] also discusses the treatment of interferences

and, in a second paper, the response under non-zero current conditions.

The most important feedback from the successful application of theoretical principles to practical problems is the suggestion of new lines of in- vestigation. A good example of this is the work of Eisenman on

cation-responsive glass electrodes [53]. The successful explanation of al- ready known facts is insufficient. At the present, however, the solution of

problems associated with the production of heterogeneous membrane

electrodes appears to require a better understanding of such properties of

finely divided solid materials as conductivity, non-stoichiometry and defect structure and how these may be controlled by suitable preparative

procedures, doping, etc. and which of them are critical for the production

of successful electrodes.

V. Acknowledgment

I am grateful to Dr. A. M. G. Macdonald (Birmingham) and Dr. K.

Toth (Veszprem) for reading and commenting on the manuscript.

VI. References

[ I] Sollner, K., Ann. N. Y. Acad. Sci. 148, 154(1968).

[2] Hills, G. J., in Reference Electrodes, D. J. G. Ives and G. J. Janz, Eds., Academic

Press, N. Y., 1961, pp.41 1-432.

[3] Lakshminarayanaiah, N., Chem. Rev. 65, 49 1 (1965).

[4] Ross, J. W., paper presented at the Symposium on Ion-Selective Electrodes, NBS,Jan. 30-31, 1969.

[5] Wyllie, M. R.,and Patnode, H. W.,.l. Phys. Chem. 54,204(1950).

[6] Bose,S. K.,J. Indian Chem. Soc. 37, 465 ( 1 960).

[7] Basu, A. S., J. Indian Chem. Soc. 39, 619 ( 1962); ibid. 35, 45 I ( 1958).

[8] Hale, D. K.,and McCauley, D. J., Trans. Faraday Soc. 57, 135 (1961).

[9] Joshi,K. M.,andSuryanarayana, N. P., J. Indian Chem. Soc. 45, 537 ( 1 968). [10] Parsons, J. S., Anal. Chem. 30, 1262 (1958). [II] Pungor, E.,Toth, K.,and Havas,J., Hung. Sci. Instr.3, 2 ( 1 965).

[ 1 2] Pungor, E., Havas, J., and Toth, K., Acta Chim. Hung. 41, 239 ( 1 964).
106 ION-SELECTIVE ELECTRODES

1 3] Pungor, E., and Havas J., Acta Chim. Hung. 50, 77 (1966).

14] Tendeloo, H. J. C. and Krips, A., Rec. Trav. Chim. 76, 703 (1957).

1 5] Tendeloo. H. J. C. and Krips, A., Rec. Trav. Chim. 76, 946 (1957).

1 6] Tendeloo, H. J. C, and Krips, A., Rec. Trav. Chim. 78, 177(1 959).

1 7] Tendeloo, H. J. C, and van der Voort, F. H., Rec. Trav. Chim. 79, 639 ( 1 960).

18] Cloos, P., and Fripiat, J. J., Bull. Soc. Chim.Fr. 423 (1960).

19] Shatkay, A., Anal. Chem.39, 1056(1967); Bloch. R., Shatkay, A., and Saroff, H. A., Biophys. J. 7, 865 (1967). 20] Buchanan, E. B., and Seago, J. L., Anal. Chem. 40, 5 1 7 ( 1 968). 21] Fischer. R. B..and Babcock, R. F., Anal. Chem. 30, 1732 (1958). 22] Hirsch-Ayalon, P., J. Polym. Sci. 23, 697 (1957): Rec. Trav. Chim. 79, 382 (1960). 23] Geyer, R., and Syring. W., Z. Chem. 6, 92 ( 1 966). 24] Morazzani-Pelletier. S..and Baffier, M. A., J. Chim. Phys. 62, 429 ( 1 965). 25] Pungor. E., Havas, J., and Toth, K.,Z. Chem. 5, 9( 1 965). 26] Pungor, E.. and Hollos-Rokosinyi, E., Acta Chim. Hung. 27, 63 ( 1 96 1 ). 27] Macdonald, A. M. G., and Toth, K., Anal. Chim. Acta41, 99 (1968). 28] Pungor, E., and Toth, K.. Mikrochim. Acta, 565 ( 1964). 29] Pungor, E., Szepesvary, E.,and Havas, J., Anal. Lett. 1,213 (1968); also Pungor, E., and Szepesvary. E., Anal. Chim. Acta 43, 289 (1968). 30] Farsang, G., Hung. Sci. Instr. 12, 22 (1968). 31] Weser, A., and Pungor, E., Proc. IMEKO Symposium on Electrochemical Sensors, Veszprem, Hungary, 1968, pp.99- 1 10. 32] Havas, J., Papp, E.,and Pungor, E., Magy. Kem. Foly. 73, 292 (1967). 33] Havas, J., and Pungor, E., Proc. IMEKO Symposium on Electrochemical Sensors, Veszprem, Hungary, 1968, pp. 79-88.

34] Rechnitz, G. A., Kresz, M. R., and Zamochnick, S. B., Anal. Chem. 38, 973 ( 1 966). 35] Rechnitz, G. A., and Kresz, M. R., Anal. Chem. 38, 1787(1 966). 36] Pungor, E.. Anal. Chem. 39, 29A ( 1 967). 37] Covington, A. K., paper presented at the Symposium on Ion-Selective Electrodes, NBS.Jan. 30-31, 1969. 38] Pungor, E., Toth, K., and Havas, J., Mikrochim. Acta, 689 (1966). 39] Rechnitz, G. A., Chem. Eng. News 45, 146 (1967). 40] Nicolsky, B. P., Acta Physicochim. USSR 7, 597 (1937); see also Isard, J. O., in Glass Electrodes for Hydrogen and Other Cations, G. Eisenman, Ed., Dekker,

New York. p. 64. 41] Eisenman, G., Rudin, D. O., and Casby, J. U., Science 126,831 (1957). 42] Toth. K., and Pungor, E., Proc. IMEKO Symposium on Electrochemical Sensors, Veszprem, Hungary, 1968, pp. 35-50. 43] Bishop, E., and Dhaneshwar, R. G., Analyst (London) 88; 424; 432; 442 (1963). 44] Csakvari, B., and Meszaros, K., Hung. Sci. Instr. 11,9(1 968). 45] Rechnitz, G. A., Lin, Z. F., and Zamochnick, S. B., Anal. Lett. 1, 29 ( 1 967). 46] Pungor, E., Schmidt, E., and Toth, K., Proc. IMEKO Symposium on Electrochemical Sensors, Veszprem, Hungary, 1 968, pp. 121-1 34. 47] Ives, D. J. G., in Reference Electrodes, D. J. G. Ives and G. J. Janz. Eds., Academic Press, New York, pp. 381-383.

48] Hseu,T-M.,and Rechnitz, G. A., Anal. Chem. 40, 1055 (1968). 49] Macdonald, A. M. G., private communication, 1968. 50] Kolthoff, I. M., and Sanders, H. L.,.l. Amer. Chem. Soc. 59, 4 1 6 ( 1 937).

5 I ] .lanz, G. J., and Ives, D. J. G., Ann. N. Y. Acad. Sci. 148, 210 (1968). 52] Buck. R. P.. Anal. Chem. 40, 1432; 1439(1968).

53] Eisenman, G., in Glass Electrodes for Hydrogen and Other Cations, G. Eisenman,

Ed., Dekker, New York, 1967, Chapter 9.
CHAPTER 4

REFERENCE ELECTRODES

Arthur K. Covington

Department ofPhysical Chemistry

School ofChemistry

University of Newcastle

Newcastle upon Tyne, England

I. Introduction

A two electrode system is the sine qua non of all measurements on elec- trochemical cells, but usually interest is directed more toward one elec- trode than the other; this other is called the reference electrode, and it is mandatory that its function should be thoroughly understood.

To judge from reading the literature on ion-selective electrodes, too

often the only reference electrode used is the saturated or 3.5M KCl

calomel, perhaps with an additional salt bridge if chloride is incompatible

with the test solution. It is assumed to be an electrode of invariant (fixed)

potential with no variation of liquid junction potential when the test solu- tion is varied or replaced by a standard or calibrating solution. For initial appraisal of a new electrode and many other purposes, this procedure

may be adequate, but the reference electrode must not be considered

unimportant in spite of temptation to do so. In fact, it is significant that in commercial practice, trouble shooting of pH problems reveals that it is the users' lack of attention to the reference electrode aspect of control

processes which is the cause of much malfunctioning.

With most ion-selective electrodes, the effective operational range is restricted to four or five decades of concentration (—300 mV for a univalent ion), whereas in the familiar case of pH measurements about a dozen decades or some 720 mV are involved. With divalent ion responsive electrodes the millivolt range is further reduced by a factor of two.

Invariably, with the new ion-selective electrodes, measurements are required with greater precision than for most pH measurements and

reference electrode considerations cannot be disregarded.

As indicated above, a reference electrode will be defined as the elec- trode which is not of primary interest in the cell. A monograph with the

title Reference Electrodes appeared in 1961 which provided a valuable

critical compilation of the properties of many electrode systems [ 1 ]. The

editors' definition of a reference electrode was somewhat broader than

that adopted here, being effectively any electrode used in combination to obtain thermodynamic information. In this context, the properties of

107
108 ION-SELECTIVE ELECTRODES

nearly all known electrode systems apart from metal-metal ion and certain

amalgam-metal ion electrodes were exhaustively reviewed [1]. Consequently, the discussion in this chapter will be restricted to points particularly pertinent to ion-selective electrodes. The essential features of

the most important reference electrode systems will be outlined and work

since 1961 reviewed in some detail. First, however, we shall discuss the

methods of utilizing the available reference electrodes in ceils of various

designs. In the final section, the problems of liquid junction potentials and

of temperature effects in non-isothermal cells will be discussed.

Janz and Ives [2] have given the three main requirements for satisfac- tory reference electrode systems: 1) reversibility, 2) reproducibility, and

3) stability, which are, as they state, interrelated quantities. The quantitative measure of the first of these is the exchange current; unless a

reference electrode has a high exchange current, its potential will depart

from its equilibrium value when current demands are made upon it. These

will depend on the measuring circuit in potentiometric applications and

may become important for miniature electrodes and at low concentrations

of the potential-determining ion. Reproducibility covers two aspects: the

ability of a particular electrode specimen to respond according to the

Nernst equation without temperature- (or concentration-) change hysteresis, and the feasibility of establishing a standard method of electrode

preparation, which will produce electrodes on one or many occasions that group acceptably about a mean potential, i.e., show small bias potentials.

The third requirement, stability, is self explanatory, referring also to the

useful life of an electrode system. How closely it is necessary to satisfy

these three basic requirements depends upon the use to which the

reference electrode is put; which we will consider in the next section. For

example, it may be possible to tolerate slow changes in the standard

potential of electrodes (e.g., aging of silver-silver chloride electrodes) if this process is slow compared with the time of measurements.

II. Classification of Reference Electrodes and Their Usage

Most of the reference electrodes to be considered in this chapter are electrodes of the second kind, that is, anion reversible. Included in this category is the case where the metal is amalgamated. There are, apart

from the hydrogen electrode and perhaps the quinhydrone electrode

which is largely out of favor in the West, few cation-responsive reference

electrodes. Such cation-response electrodes that are well behaved tend to be of specialized usefulness, e.g., Hg|+|Hg, Ag+|Ag, Pb2+|Pb(Hg),

and Cd2+|Cd(Hg). The alkali-metal amalgam electrodes would be of considerable use if it were not for their disadvantage of hydrogen evolution.

However, these amalgam electrodes have received more attention

recently [3,4]. Sodium- and potassium-responsive glass electrodes are a
REFERENCE ELECTRODES 109

better proposition but only under limited circumstances could they be

considered as reference electrodes.

Anion-reversible electrodes are more generally useful than

cation-responsive reference electrodes, but even so the absence of nitrate and perchlorate reversible conventional systems makes the choice

somewhat restricted. This is presumably one reason for the attractiveness

of electrodes of fixed potential such as the saturated calomel, particularly

in its commercial forms. The utility of this electrode for pH measure- ments should not, however, make it a universal choice for ion-selective

electrode measurements, since the problem of the reference electrode to use is basically one of cell design. With particular relevance to ion-selective electrodes, we shall now consider six methods of reference electrode

usage.A. Internal Reference Electrodes for Ion-Selective

Electrodes

Ion-selective electrodes and the glass electrode in particular are ac- tually electrode assemblies, in which a stable inner reference system is required. It seems to be essential that a well-defined potential determining

process takes place at the inside surface of the ion-selective "membrane,"

but mercury has proved satisfactory in the case of the glass elec- trode [5,6] and a solid silver chloride coating has been described [7]. The silver-silver chloride electrode in hydrochloric acid or in a

chloride-containing buffer solution is commonly used for hydrogen-responsive glass electrodes, and sodium-responsive electrodes

function with an acid filling not containing sodium ions, because the glass

shows some hydrogen ion function at low pH. The question of the solvent

used for the inner reference solution of the glass electrode, when it is to be

used in partially aqueous media, has received some attention recently by

several French workers [8-10] and by Ritchie and his collaborators [11].

Bottom and Covington [6] have recently investigated this problem with

the surprising findings that the potential difference on transferring a glass

electrode between two partially aqueous solutions can depend on the sol- vent of the inner solution. This may have some implications for work on

the newer ion-selective electrodes.

The silver-silver chloride electrode is used for some ion-selective elec- trodes. For example, in the lanthanum fluoride electrode [12], the inter- nal system is Ag; AgCl|NaCl, NaFlLaFs

However, for some electrodes a cation-responsive internal reference is used, e.g., Ag I AgNOa I Ag2S.
110 ION-SELECTIVE ELECTRODES

When there is an alternative between a possible cation or anion system,

there may be a difference in behavior which could be significant of the

mechanistic process involved at the "membrane."

B. Use of Reference Electrodes for Direct Comparison with an

Ion-Selective Electrode Supposedly Reversible to the Same

Ionic Species

The only unequivocal way of showing that a new electrode responds to a certain ion, that does not require knowledge of activity coefficients, is by a direct check against another electrode responsive to the same ion. This technique has been used with hydrogen-responsive glass electrodes

{e.g., [6,13]). The emf of the cell glass I X I H.; Pt should be the same irrespective of X, provided it contains hydrogen ions,

if the glass electrode is behaving solely as a hydrogen ion responsive elec- trode. If X contains sodium ions and at high pH the electrode shows some

sodium function, then there will be some change in emf A similar

technique has been employed to determine the silver response of glass

electrodes using the silver electrode [ 14] , and the sodium response using a sodium amalgam electrode [15]. The deuterium gas electrode has been

used [1 6] to check the deuterium ion function of hydrogen ion responsive

glass electrodes. This technique has not been sufficiently explored with

the new ion-selective electrodes, apart from the work of Alfenaar and

Bates [17]. Of course, this technique is inapplicable if no conventional

electrode system exists responsive to the ion in question, as is the case for

the nitrate and perchlorate liquid ion exchanger electrodes.

C. Use of Reference Electrodes Reversible to Another Ion;

Often That of an Added "Inert" Electrolyte

Few measurements are made on solutions containing a single elec- trolyte, and it may not be possible to choose an electrode reversible to its counter ion. Thus it may be necessary and sometimes advantageous to add an electrolyte to a solution of interest in order to make the determination possible. The most common example of this is the addition of sodium

chloride to the Harned cell for the determination of the pK of a weak acid

(the basis, in fact, of pH scale determinations) so that the silver-silver chloride reference electrode may be used, e.g., Pt; H2 I HA, NaA, NaCI | AgCl; Ag

where A- is the anion of a weak acid [18].
REFERENCE ELECTRODES 111

If it is advantageous to buffer a solution to facilitate the determination

with an ion-selective electrode, then the hydrogen gas electrode could be

used as reference electrode. The use of a glass electrode as an alternative

to the hydrogen electrode is placed under Section II.D. below because of

the need to standardize it, that is, to eliminate its "standard potential."

D. Use of Reference Electrodes as ''Bridging" Electrodes

All electrode determinations are concerned with emf differences and

concentration differences, although this fact is obscurred by referring the

emf to a standard state, an unreal solution with an associated emf, E°. This can be exemplified for the Harned cell above, because the deter- mination of the pK requires E° to be obtained from the cell

Pt; H2 I HCl I AgCl; Ag.

Hence, we are interested in a difference in emf between two cells. As

discussed below, the standard potential of the silver-silver chloride elec- trode can vary by as much as 0.2 mV. Hence, it has been suggested [19] that it should be redetermined for each set of newly prepared electrodes

by making measurements in the cell

Pt; H2 I HCl(m = 0.0100) | AgCl; Ag

assuming a value for the activity coefficient of hydrochloric acid at 0.0 1 m.

In a sense, the silver-silver chloride electrode here is being used as a

"bridging" electrode.

The foregoing serves as an introduction to the technique of using a glass

electrode and, indeed, any ion-selective electrode in this way. Zielen [20]

made measurements on the cells

Pt; H2 I HCl(m) I glass

Ag; AgCl I HCl(w)|gIass

where the same glass electrode is transferred between the two solutions

of HCl of the same molality. By this technique, dissolved silver chloride

is prevented from reaching the hydrogen gas electrode and being reduced;

it has no effect on the glass electrode. Zielen described his technique as being one for eliminating the effect of a liquid junction potential produced

by dissolved silver chloride. This technique was also used by Covington,

Dobson and Wynne-Jones [21] as a check on the effect of the more solu-
112 ION-SELECTIVE ELECTRODES

ble mercurous sulfate in sulfuric acid solutions. If the second cell above were instead [20]:

Pt; H2 I HX I glass

then the method is basically the application of Section B above.

A similar technique has been used by Srinivasan [22] with

sodium-responsive glass electrodes to determine the standard potential of

the mercury-mercurous picrate electrode using the cells glass (Na) | NaCl | AgCl; Ag

glass (Na) | NaPc | Hg2Pc2; Hg

where Pc~ is the picrate anion. The remaining two categories are con- cerned with cells with liquid junctions.

E. Use of Reference Electrodes of (Ideally) Invariant

Potential

The use of the saturated calomel electrode has already been discussed

in Section I. To be specific, we will take the example of the operational

pH cell: Pt; H2 I S 1

1 KCl(sat) | HgsCU; Hg

where S is a standard solution of assigned pH(S). The emf of the cell is given in terms of pH(S) by, [23]

(RT\n \ OlF)pU{S) = E-(E°' + Ej) (1)

where Ej is the liquid junction potential and E°' includes, besides the E°of

the cell, a term involving the single ion activity of chloride ion in the

potassium chloride. The term {E°' + £}) is often referred to as the "stan- dard potential" of the calomel electrode. Clearly, since the liquid junction

potential depends on the solution, S, the value of the standard potential

will be somewhat dependent on the solution used to determine it. Values

of iE°' + Ej) are tabulated but they are rarely required, since as in pH

measurements, the measurement is comparative, and the cell effectively

involved is: Pt; H2 I X II KCl(sat) || S | H2; Pt (£x - Es)

where X is a solution of unknown pH and

pH(X)-pH(S) + (Ex-EsjF//?rln 10 (2)
REFERENCE ELECTRODES 113

Hence, if the residual liquid junction potential ^.Ej= Ej(x) - £j(s) is zero, the

standard potential cancels out. If AEj is not zero, the error will be incorporated in pH{X). Similar considerations are applicable to an operational

determination of plon [24] using ion-selective electrodes. The question

of liquid junction potential variation will be discussed in Section IV. Besides the system KCl(sat)|Hg2Cl2; Hg, different potassium chloride

concentrations, e.g., 3.8, 3.5, 1.0, and O.IM are sometimes used, the last two being out of favor. Sodium chloride [25] and, for ethylene diamine

media, saturated lithium chloride [26J have also been used. Some workers

prefer the system KCl(sat), AgCl(sat) | AgCl; Ag, and the system

K2S04(sat) I Hg2S04; Hg is available commercially for cases where

chloride contamination cannot be tolerated. Otherwise, an intermediate

salt bridge of ammonium nitrate is used with the saturated calomel elec- trode.

It is possible to conceive other potential invariant systems which might

be more appropriately used with ion-selective electrodes but, as emphasized earlier, this is a problem of whole cell design, and we shall defer further discussion to the section dealing with liquid junction potentials, giving only an example here [27]

:

LaFslNaCl, NaF||NaCl, HCIIH2; Pt

F. Use of a Second Similar Ion Selective Electrode as a Reference Electrode

This method is an extension of the well-known homo-ionic concentration cell with two similar electrodes, e.g., Ag; AgCl|CaCl2fmi)||CaCl2(w2)|AgCl; Ag

to ion-selective electrodes, e.g., LaF3 I KF(mi) || KF(m2) | LaFs

and an intermediate salt bridge may be inserted.

Such cells may be adapted for potentiometric titration determinations.

A good example of this is the work of Durst [28] using the cell:

LaF:, |F^, KNO3(0.1M) || KNO,(0.1M) || KNO3(0.1M), F7 | LaF,

where the left hand side of the cell is kept constant and comprises a micro-amount of fluoride-containing solution. The solution in the right

hand side compartment is titrated, adjusting the fluoride ion concentration

until the cell emf is zero. The technique is termed linear null-point poten-
114 ION-SELECTIVE ELECTRODES

tiometry (LNPP). It is necessary to take into account any asymmetry

potential difference, including differences in the internal reference

systems of the two fluoride electrodes. This can be measured by directly

comparing the two electrodes in a fluoride solution (bias potential deter- mination). Since the new ion-selective electrodes tend to have much

lower resistances than do glass electrodes, the problem of the measure- ment of potential with two high resistance electrodes and grounding dif- ficulties are not so serious.

III. Preparation and Properties of Some Important Reference Electrodes

A. The Hydrogen Gas Electrode

The hydrogen gas electrode is worthy of discussion first, not only

because it is the electrode whose standard potential is conventionally set

at zero at all temperatures in order to tabulate standard potentials of other

electrodes, but because it is probably the most reproducible electrode

which we have available. Bias potentials are always less than lOjitV for freshly prepared electrodes.

The hydrogen electrode consists of a platinum foil, the surface of which

is able to catalyze the reaction

H + + e-^ 1/2 H2

which does not occur in the solution phase. Platinum black is the most

useful catalyst. It is usually deposited from a 1-3% solution of

chloroplatinic acid with the addition of a small quantity of lead acetate as suggested by Popoff, Kunz and Snow [29]. The additive is not essential as Hills and Ives [30] showed, but it is desirable, as electrodes prepared

using it have a longer life and are less susceptible to poisoning. The elec- trode is poisoned by traces of sulfide and cyanide, but when this occurs,

the potential is so far from the expected value for there to be no doubt

about an electrode malfunction. Drifting potentials are observed when the

chemical reduction of species such as benzoic acid, nitrophenols, etc., can

take place at the catalyst surface. This can be overcome, as in the case of

measurements on the standard buffer substance potassium hydrogen

phthalate, by using a palladium black deposit, which has a lower catalytic

activity. If reduction of some solution species is suspected, two elec- trodes of different catalytic activity may be employed so that differences

in potential and variations with time would confirm suspicions. This

technique has been used for concentrated (5M) perchloric acid solutions

[31], and contrary to reports in the literature, hydrogen gas electrodes can be used in these solutions.
REFERENCE ELECTRODES 115

The twin roles of the platinum black and the platinum substrate were

nicely demonstrated by Hills and Ives [30] with their catalyst electrode.

They showed that the potential of an electrode consisting of a bright

platinum cone with platinum black dispersed in solution by the continu- ous bubbling of the hydrogen gas agreed to within 10 />tV with the potential of a conventional hydrogen electrode.

The hydrogen electrode is not as difficult to use as might be imagined.

A supply of pure hydrogen gas is required, and it may be noted that palladium diffusion purifiers are now commercially available. A means of

saturating the solution with hydrogen gas without changing its composition is required, but a wash-bottle with a fritted disc bubbler and filled with the cell solution is perfectly adequate. Potential readings are cor- rected to the standard atmospheric partial pressure of hydrogen gas from

knowledge of the vapor pressure of the solutions and the prevailing

barometric pressure. The bubbler depth correction noticed by Hills and

Ives [30] can ordinarily be ignored as insignificant. Further details can be

found in Ives and Janz's monograph [1] or that of Bates [32].

B. Silver-Silver Halide Electrodes

Next to the hydrogen electrode, the silver-silver chloride electrode is probably the most reproducible and certainly the most reliable and convenient reference electrode. It has been the subject of many reviews

[33-35], the most recent being that of Janz and Ives [2]. The electrode reaction is AgCl + ^--^ Ag + Cl-.

The solubility of silver chloride in water is about 10"^ mol liter"' at 25 °C which sets a lower limit on the use of the electrode for determining

low chloride concentrations. The solubility in saturated potassium

chloride solution is such (about 6x lO"'^ mol liter-' at 25 °C) that it is necessary to presaturate the solution with silver chloride, otherwise the

electrode becomes stripped of its coating.

Of the several methods of preparing silver-silver chloride electrodes

only three need concern us here:

1 . A silver wire is coated with silver chloride by making it the anode

in a suitable chloride solution, usually 0. IM hydrochloric acid or potassium chloride. Electrodes prepared in this way are suitable for potentiometric titrations or as inner reference electrodes for membrane electrodes.

Strains and probably impurities introduced in the drawing process cause

the bias potentials of such electrodes to be fairly high (±5 mV), but this

is of no consequence in the applications mentioned.
116 ION-SELECTIVE ELECTRODES

2. Silver is plated on a platinum substrate from a cyanide bath, and the

silver chloride coating is formed as described above. These electrodes are

free of the objections raised above. Their response times are short so, when this is important, for example, in potentiometric titrations, they are preferable to the thermal-electrolytic type {vide infra).

3. In the thermal-electrolytic type, silver is formed by heating a paste

of silver oxide on a platinum substrate, usually wound in the form of a

spiral. Part of the spongy silver mass is converted to chloride by the elec- trolysis process described above. Because the silver is porous, the elec- trodes tend to be rather sluggish and show concentration polarization ef- fects due to the occlusion in the pores of electrolyte from the chloridizing process. They can, however, be prepared with a very small range of bias

potentials (±20)LtV), provided that the silver oxide, prepared from the

addition of sodium hydroxide to silver nitrate solution, is washed very

well. Electrodes with higher bias potentials can sometimes be brought

into line by heating them for two hours in distilled water at 50-60 °C

[36]. In acid solutions, the silver-silver chloride electrode is sensitive to traces of oxygen, which is attributed to the reaction: 2 Ag + 2H+ + 2C1- + 1 /2 O2 ^ 2 AgCl + H2O

which causes a decrease in the chloride ion concentration. In high precision work, nitrogen is bubbled through the cell solutions before and dur- ing measurements. This procedure is not necessary when work of a precision of less than 0.3 mV is required or for neutral solutions, although

Manov et al. [37] state that the potential is raised 1.5 mV when a satu- rated potassium chloride solution is saturated with air. The electrode is very sensitive to traces of bromide impurity. The effect has been studied by Pinching and Bates [38], who found that 0.064 mole

percent of potassium bromide affected the bias potential of an electrode

(relative to an electrode in a Br~-free solution) by about 1 mV. This large

effect is attributed to the fact that silver chloride and silver bromide form

solid solutions. The effect of iodide is much less, probably because the

iodide and chloride of silver do not form solid solutions. The effect of

bromide impurity is to change the standard potential of the electrode. This conclusion is a by-product of the painstaking work of Giintelberg,

who repeated [39] most of his earlier work [40] on the variation of the

activity coefficient of hydrochloric acid in the presence of alkali metal

chlorides at constant molality (0.1m) when he discovered that his chlorides were contaminated with bromide. Pinching and Bates [38]

have described a method of preparing chlorides free from bromide impurities and a sensitive colorimetric test for detection of small traces of

bromides.
REFERENCE ELECTRODES 117

In spite of using apparently identical preparative procedures, it has

been repeatedly found that thermal-electrolytic electrodes prepared in dif- ferent, and from time to time in the same, laboratories differ slightly in standard potential. It is usual to prepare batches of electrodes, discarding

electrodes that show wide divergences from the mean. The mean potentials of separate batches may differ by up to 0.2 mV [41,42]. For this reason, it has been suggested by a group of eminent physical chemists

[ 1 9] that the standard potential of the electrode be redetermined for all new precise investigations by making a single measurement at 25 °C in 0.0100 molal hydrochloric acid against a hydrogen gas electrode. The activity coefficient of hydrochloric acid to be assumed is 0.904. For other

temperatures, this principle can be extended by using the values given in Table 1 , which have been calculated from the best values for the activity

coefficients of 0.0100 molal hydrochloric acid [43], by noting that Guggenheim's specific interaction coefficient [44] is almost independent

of temperature in the range 0-55 °C. If this suggestion of redetermining

the standard potential each time is adopted, it may not be necessary to avoid traces of bromide except in work of the highest precision.

For convenience, standard potentials for 0-95 °C are given in Table 2. The standard potential iE°'-\-Ej) for the electrode system KCl(sat),

AgCl(sat) I AgCl; Ag was found to be 198.1 mV at 25 °C by Manov,

DeLoUis and Acree [37] . Measurements at other temperatures are not

available apart from a single measurement at 60 °C [45] of 165.7 mV.

Lastly, we may mention that the silver-silver bromide and silver-silver iodide electrodes may be used with care and comparable precision, but

the effects of oxygen are much more serious. Standard potentials have

been determined recently at the NBS [46,47] and are given in Table 2. Variations of standard potential between preparations can occur, and activity coefficient values for 0.01 rnolal acids are given in Table 1 , thus per- mitting checks to be made.

Table 1. Activity coefficients of HCl, HBr and HI at 0.01 mol kg~^

(required for the determination of the standard potentials

of silver— silver halide electrodes).

>^HC1 >^HBr ^HI

0 0.907 0.910

10 0.906 0.909

25 0.904 0.906 0.907

40 0.901 0.904

50 0.899 0.902
118 ION-SELECTIVE ELECTRODES

C. The Mercury-Mercurous Chloride (Calomel) Electrode

The calomel electrode as a chloride-reversible electrode was extensively used before 1 930, but later it was abandoned in favor of the more relia- ble silver-silver chloride for all precise work. The ideally potential-invari- ant saturated or 3.5M calomel electrode has always ubiquitously enjoyed

popularity. Prepared by grinding calomel, mercury and a little potassium

chloride solution together and placing the resultant slurry in a layer about

1 cm thick on the surface of mercury, this electrode will be called the classical electrode. Hills and Ives [48] argued that this thick paste was un- necessary and probably detrimental, and motivated by the idea that a

liquid metal substrate for an electrode of the second kind should be better

than a solid metal, reinvestigated the calomel electrode. They devised a new method of preparation in which calomel and mercury were shaken

together in the dry state and a small quantity introduced on to a mercury

surface where it immediately spread. Solution was then added carefully

to this "skin" electrode. Hills and Ives' [48] results with the

hydrogen-hydrochloric acid-calomel cell were of outstanding precision.

The electrode is very sensitive to traces of oxygen, which cannot be ex- plained entirely by the reaction:

2Hg-f 2HC1 + 1/2 O2 ^ Hg2Cl2 + H2O

because at small concentrations of gas, the effect is reversible. A second

important experimental point was the prevention of the formation of an- nular solution films between mercury and the glass and, thus out of

equilibrium with the bulk of the solution, by the expedient of silicone treatment of the glass.

Hills and Ives' standard emf at 25 °C was reproduced by Schwabe and

Ziegenbalg [49] but Grzybowski [50] found a value 0.2 mV higher.

Additional indications that the electrode was not as good as at first thought came from the failure to use it at other temperatures because of

marked temperature hysteresis. In a further series of investigations,

which have been summarized [51], Ives and his coworkers traced the cause of the troubles to the disproportionation of calomel:

Hg2Cl2^Hg+HgCl2

and the resultant formation of mercuric complexes in solution. This reaction is slow and over two days leads to a rise in potential of about

0.2 mV. Hills and Ives' readings were taken after about 6 hours whereas

Grzybowski's were "next-day" values. This led to the concept of "first" and "second day" calomel potentials. Temperature hysteresis effects arise from the solution still containing dissolved mercuric species formed
REFERENCE ELECTRODES 119

at higher temperatures when the electrode is returned to lower temperatures. Covington, Dobson and Wynne-Jones [43] essentially supported Ives' findings and demonstrated spectrophotometrically the gradual accumulation of mercuric species in solution (Fig. 1). Using much smaller ratios of

surface area of mercury to volume of solution than Hills and Ives [48] (as

had also Grzybowski [50]), Covington et ai used two to three times more of the dry calomel-mercury mixture for the smooth skin electrode of

Hills and Ives [48]. This has a definite advantage at higher temperatures. By comparison of all available data for the hydrogen-calomel

and hydrogen-silver chloride cells, Covington et al. concluded that Grzybowski's data at temperatures other than 25 °C, which on reanalysis were in good agreement with their own less extensive data, were probably

the most reliable. For convenience, these values are given in Table 2; it is considered that restricting the accuracy of the stated values to 0. 1 mV

is justified in view of the difficulties associated with using this electrode.

There have been numerous electrode kinetic studies of the calomel

electrode. Armstrong, Fleischmann and Thirsk [52] , who give references

to earlier work, conclude that two competing processes occur in the

321

emf

(mV)

320

1 week^ ^ lo

33

Cp 3-

O 3O3^ •••

••••

-J L J I l_

HgCl2

ppm

o 10 20

time, hours

Figure 1. Variation of the calomel electrode potential with time (O Covington et al. [43] type of electrode with thicker calomel layer; 3 Hills and Ives' type electrode) compared with the increase in mercuric species in solution with time, measured spectro- photometrically at 230 nm by calibration using stock solutions of mercuric chloride in 0.5 m HCI (after Covington, Dobson and Wynne-Jones [43]).
120 ION-SELECTIVE ELECTRODES

[if ~

O K

00

LTD CO lO

00 t> CO

CO 247, i

234. S5

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No

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I I I I

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oc

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tT O CD 00 05 lO g O 05 00 CD CD

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REFERENCE ELECTRODES 121

anodic polarization of mercury in chloride solutions, the dissolution of

mercury as HgCl|- and the formation of calomel. The complex ion

species is identified as HgCll" at concentrations greater than 1 mol

liter-i on the basis of Dry and Gledhill's studies by conductance [53],

other species being present in much too low concentration to account for the observed kinetics. Armstrong et al. [52] consider that the time dependent effects of the "equilibrium" calomel potential are due to a mixed

potential, the two competing processes being:

2Hg+2Cl-^Hg2Cl2 + 2^-

Hg + 4Cl-^HgC12- + 2eIt is not clear, however, why the electrode should take so long to come to equilibrium with mercuric species in solution if the process responsible is purely diffusional. Figure 1 shows that the concentration of mercuric species continues to rise after the electrode has reached a steady potential,

and these results suggest that other factors may be involved such as

recrystallization of the calomel.

It is also not clear whether the above outlined difficulties associated

with the calomel electrode in acid solution are relevant to its functioning

in neutral potassium chloride solution. Armstrong et al. [52] noted a

similar kinetic behavior in KCl solutions. Covington et al. [43] found some differences between the potentials of the calomel-silver chloride cell when different chlorides were used, and it is conceivable that the

presence of different cations will affect the stabilities of the various mercuric chloride complexes present. It must be emphasized, however, that

in these studies one is concerned with small differences of the order of

0.2 mV only, and other effects notably that of oxygen can easily swamp

these. There is no reason to believe that the classical calomel electrode

will not be in equilibrium with mercuric species, but the process of grinding calomel and mercury together wet will aid any process involving at- mospheric oxygen. Alner, Greczek and Smeeth [45] have used the improved calomel electrode in a study of the operational pH cell and a

variety of buffer solutions. They reported that the behavior of the calomel

electrodes was satisfactory and calculated values for the standard potential {E°' + Ej) of the saturated calomel electrode using the NBS values for the pH of potassium hydrogen phthalate standard buffer from 0-50 °C

[54]. They believe that these values (given in Table 2) are equilibrium

values, but "the measurement of these potentials was only a small part of

the present work and the calomel electrodes were discarded as soon as

their potential values began to drift." The electrodes "remained stable to within ± 10 /LtV for at least ten days and much longer at the lower temperatures." This is remarkably good for a cell involving a liquid junction.
122 ION-SELECTIVE ELECTRODES

Although not stated in the paper [45] where it is said that the calomel

electrodes were prepared "according to the recommendations of Ives and

his coworkers," it is significant that Greczek states [55] that a 5 mm

layer of calomel was used instead of 0.5 mm. This procedure was stated not to affect the equilibrium potential nor the time taken to achieve it but

did greatly improve the stability of the electrode at 40 and 50 °C. It will be recalled that a similar thicker layer was preferred by Covington et al. [43].

According to Shams El Din and Kamel [56], another source of time

variation of calomel electrodes is impurities such as zinc, cadmium, tin, lead or copper in the mercury. They conclude that time must be allowed

for impurities to diffuse to the mercury surface and dissolve in the solu- tion phase. This effect is unlikely to be present in the precision studies

mentioned above but could be a factor with commercial electrodes. In the

author's experience, commercial electrodes can show large bias potentials

when intercompared as well as fluctuations from day to day. Sibbald and

Matsuyama [57] report a standard deviation of ±0.25 mV over 12 days

with a commercial electrode. Normally for pH measurements such varia- tions do not matter if standardization is carried out frequently. It must not be assumed, however, that the glass electrode is always to blame for

variations.

The calomel electrode cannot be recommended as a reference electrode

responsive to chloride ions. The silver-silver chloride electrode is far more reliable and convenient to prepare. Even as a potential-invariant

electrode, the calomel electrode has distinct limitations, principally due

to temperature hysteresis effects (see Fig. 3). It is to be hoped that it will gradually be replaced by more reliable alternatives such as the thallium

amalgam-thallous chloride electrode (Section 1 1 I.E.). D. Mercury-Mercurous Sulfate Electrode

Some commercial suppliers include the mercury-mercurous sulfate electrode in saturated potassium sulfate in their catalogs of reference elec- trodes. Mattock [58] gives the standard potential {E°' + Ej) of this elec- trode system as 658 mV at 22 °C, but no measurements seem to be

available at other temperatures.

Ives and Smith [59] comment that in spite of the tendency to hydrolyze

and its rather high solubility, the mercury-mercurous sulfate electrode is "alongside the hydrogen electrode in being capable of outstanding

reproducibility." It is of course one of the electrodes of the Weston

standard cell. In contrast to the calomel electrode, it needs no special

preparative procedure, except for the preparation of the sulfate electrolytically [60J.
REFERENCE ELECTRODES 123

In an investigation of the hydrogen-sulfuric acid-mercurous sulfate cell at molalities of 0.1-8.0, Beck, Dobson and Wynne-Jones [61] elegantly

demonstrated that their data were consistent with vapor pressure data at 25 °C giving a standard emf of 615.81 mV, that is, 0.45 mV higher than

Harned and Hamer's value [62]. (Note that the values given in Ref. [59] are incorrect.) Unfortunately, vapor pressure data of sufficient accuracy

are not available at other temperatures so that standard emf's at temperatures other than 25 °C cannot be obtained. Published values are those of

Harned and Hamer [62], which are incorrect at 25 °C and probably also

at other temperatures.

Harned and Hamer [62] had stated that the cell could not be used at molalities below 0.05 because of the enhanced solubility of mercurous

sulfate giving rise to the possibility of an appreciable liquid junction

potential. No experimental measurements were given in support of this assertion, and the point was reinvestigated by Covington, Dobson and

Wynne-Jones [21]. The mercurous sulfate electrode was compared with

two other sulfate-reversible electrodes and simultaneously with the

hydrogen electrode — a good example of the power of such an ap- proach. It was concluded that the mercurous sulfate electrode functioned

down to 0.01 mol kg~^ and that it was possible to determine the standard

potential of the electrode by extrapolation, provided the second dissociation constant of sulfuric acid was known and the Debye-Huckel equation

used for the ionic activity coefficients. Each of these introduces an uncertainty, for the former depends also on the value taken for the distance of

closest approach parameter in the Debye-Hiickel equation [63]. The

standard potential at 25 °C was stated to be 612.5 mV with an uncertainty

of at least ±0.3 mV. Clearly, the evaluation of the standard potential from the data at higher concentrations would be free of such uncertainty, but this must await accurate vapor pressure data in the range

0-55 °C. Until this is available, stoichiometric activity coefficients for

sulfuric acid remain unknown at temperatures other than 25 °C.

E. Mercury-Mercurous Carboxylate Electrodes

Interest in these electrodes has been revived recently and some of them

show considerable potentiality as reference electrodes, particularly in buffered solutions. Larson and his coworkers [64-67] studied the acetate and oxalate electrodes in solutions of the corresponding acids. Covington,

Talukdar and Thirsk [68] reexamined the acetate electrode in buffer

solutions and found = 51 1.3 mV at 25 °C (where subscript m refers

to molality) with only small discrepancies with Larson's early work

[65] and a later supplement [66]. Almost simultaneously, Gryzin [69]

compared the electrode in sodium acetate solutions against the saturated
124 ION-SELECTIVE ELECTRODES

calomel electrode, but his result at 25 °C is discrepant = 498.4 mV),

while Chauchard and Gauthier's [70] recent value by the same method is intermediate (E°=502 mV), where subscript c refers to molarity.

Schwabe and Glockner [71] had earlier used the electrode successfully

as an internal reference electrode for glass electrodes. From a determination versus the hydrogen electrode in Michaelis buffer (0.1 equimolar

acetic acid + sodium acetate), one can calculate E°(=511mV [68]

in support of the value first mentioned above. Schwabe [72] has also used

the electrode successfully in methanol and isopropanol solutions.

The propionate electrode has been studied by Aditya et al. [73], who

find E° = 500mV at 30 °C in good agreement with the French workers

[70], mentioned above, who also studied the formate electrode (E° = 567 mV) at25°C.

Larson and Tomsicek [67] investigated the oxalate electrode, and this work has been repeated by Srinivasan [22], whose value in oxalic acid

solutions = 417.3 mV at 25 °C) differs by 1 mV from the earlier one when recalculated with more recent values tor the dissociation constants

for oxalic acid. The electrode did not function as well in buffered solutions

for reasons not readily ascertained.

Bertram and Bone [74] determined the standard potential of the

benzoate electrode in water (solubility 0.02 mol kg-^) and in 20%

methanol-water solution (0.06 mol kg"M. In water Em = A263 mW at 25 °C whereas Chauchard and Gauthier's value [70] is lOmV higher.

(Note: EZ -£c° = 0.15 mV for all these electrodes in water at 25 °C.)

The electrodes were prepared by introducing a slurry of the mercurous

salt solution and mercury onto the mercury surface in the manner of the

classical calomel electrode. While the reproducibility of the electrodes is not high (±0.1 mV), and there are some unexplained discrepancies,

these electrodes are worthy of further consideration as reference elec- trode systems. Some care needs to be exercised in using them in solutions

that are dilute, because of possible hydrolysis of mercury ions and of

liquid junction potentials resulting from enhanced solubility (but see Section IV). Some electrode forms suitable for use with mercury-mercurous

salt electrodes are shown in Figure 2.

F. Thallium Amalgam-Thallous Chloride Electrode

The reference electrode system:

KCl(sat), TlCl(sat)|TlCl(5); Tl(Hg) was suggested by Fricke [75-77] and is commercially available

("Thalamid" electrode). It is claimed to be reproducible, usable to higher
REFERENCE ELECTRODES 1 25

Figure

a

2. Some useful electrode bed forms for mercury-mercurous salt electrodes: a. cuptype [45], b. dip type [21,43,68], c. encapsulated type, d. Thalamid [77].

temperatures (135 °C) than calomel, and moreover to be free of temperature hysteresis, which even the silver-silver chloride system is not

(Fig. 3). The principal advantage claimed is for its use in symmetrical

glass electrode cells {i.e., as internal and external reference electrodes)

when a well-defined "isothermenschnittpunkt" [76] is found close to the

"nullpunkt" of the system (these terms will be discussed in Section V).

The thallium-mercury system contains an intermetallic compound

Tl'iHgo, which disappears above about 14.5 °C [78], so above this temperature the electrode is not the usual form of the two-phase amalgam

system, liquid + intermetallic compound. An amalgam of 40 wt percent

is suggested for the reference electrode.

The solubility of thallous chloride in saturated potassium chloride is fairly high (3 x 10-^ mol liter-' at 25 °C [79]), but it is less in ammonium

chloride, which perhaps is why this is suggested as an alternative medium

[75]. Above 3.5 mol liter-' potassium chloride, the solid phase in
126 ION-SELECTIVE ELECTRODES

O** 50° 100**C Figure 3. Temperature hysteresis of calomel, silver-silver chloride and thallium amalgamthallous chloride reference electrodes (after Fricke [75]): • 3 min after drop in temperature: O 5 min after drop in temperature. equilibrium contains potassium chloride (7%) indicating complex salt for- mation [79]. The solubility of thallous chloride is a minimum at about

1 mol liter" ^ potassium chloride [79], which was the reason for selecting

this as the electrolyte in careful studies of the cell TI(Hg); T1C1|KC1| AgCl; Ag

carried out by Mussini and Longhi [80]. Standard potentials for various

amalgam concentrations in the range 0.2-39.5 mole percent and 0-80 °C were calculated. Thallium amalgams react with air, which is one disadvantage of the system. Studies of the cell Tl(Hg) I TlCl I AgCl; Ag

were made by Cowperthwaite, La Mer and Barksdale [81] at thallous

chloride concentrations below saturation (<0.01 mol kg~M in water. Thallous chloride is too soluble for the electrode system to be useful as an

electrode of the second kind responding to variations in chloride ion concentration.

Standard potentials {E°' -\- Ej) for the 40 wt percent saturated potassium

chloride electrode have not been published. If required, they could be obtained by the method used for the saturated calomel electrode [45]. The

potential relative to the saturated calomel electrode at 20 °C is 816.0 mV

[77].

i
REFERENCE ELECTRODES 127

IV. Liquid Junction Potentials

A welcome renewal of interest in the problems associated with liquid

junction potentials can be discerned during the past few years. It bears re- peating, however, that the potential across liquid junctions is indeterminate practically, being dependent on single ion activities, themselves in- determinate. A nomenclature preferable to the Ej used earlier is that of

Guggenheim [82]. The cell emf, £, is split into the thermodynamically

exact formula:

E = Eel + E(i-\- Eg

where Eei is the electrode potential given by the Nernst equation for the

cell in terms of concentrations, and for dissimilar electrodes includes the

standard emf of the cell. The diffusion potential, Ed, is given by:

Ed= {RTIF) j^'' ^(ti/zi) din rrii (3)

in which ti, zu and rm are the transference number, charge, and molality,

respectively, of the ion /, and I and II refer to the junction terminal solutions. Eg is the salt effect potential comprising both the single ion activity

coefficients (y,) from the Nernst expression and from the liquid junction

potential {Ej) where:

Ej = - {RTIF) I^^'^^'^ ^

^"^^

The most important feature of this division is that Es is a function of mean

ionic activity coefficients and is therefore in principle experimentally

determinable. Thus Eei, Ed, Es and hence E are separately calculable pro- vided certain assumptions are made about the composition variation across the boundary and the constancy of mobilities independent of en- vironment, and the necessary experimental information is available. Ej is not calculable unless some convention is adopted for single ion activities. The so-called calculation of liquid junction potentials by the Henderson,

Planck, or Lewis and Sargent equations is, in this nomenclature, a calculation of Ed. The emf of a cell involving a liquid junction is, except for homo-ionic

junctions (those between two concentrations of the same solute electrolyte), known to depend on the method of forming the junction and the

subsequent interdiffusion of the two solutions. For those cells which have

been studied, the variations are not large, being of the order of a few millivolts. Unfortunately, our knowledge is very meager and almost entirely
128 ION-SELECTIVE ELECTRODES

restricted to junctions between HCl and the alkali metal chlorides

[83-86].

Guggenheim has distinguished a number of types of junction [82] in- cluding:

a. continuous mixture, important not from the practical standpoint but

because a linear mixing form xI + (l-x)II is assumed in the Henderson

integration for Ed\

b. free diffusion formed by the natural interdiffusion of the two solutions;

c. restrained diffusion, where the length of the diffusion zone is kept

constant, and is important only because it forms the basis of the assumption made by Planck in his integration for Ed\ and

d. flowing-junctions.

Unfortunately, the type ofjunction most often used and associated with

commercial reference electrodes of "fixed" potential falls into none of

these groups. Guggenheim has referred to these as "sharp junctions of in- definite type" [82]. Invariably, the basic requirement for stability, that of

denser solution below, is not observed, and there is a flow of electrolyte,

e.g., potassium chloride, radially outward from the restraining diaphragm.

These restrained flow juncfions can take several forms [87], including a porous frit, a fiber wick, a ground glass sleeve, porous glass [88], a palladium annulus (a leaky glass-metal seal) and a cellophane membrane

[89] to mention only the commonest (Fig. 4). Although the diffusion is free, the second essenfial criterion for stability, that of cylindrical symmetry [82], is not observed and there may be irregular fluctuations of

several millivolts. Although there have been a few published accounts

[57, 90] of investigations of commercial calomel reference elements, and no doubt some more information is held by the manufacturers, it seems

that there is a need for a detailed investigation and comparison with

properly formed free diffusion juncfions [45,82,91 ]. The finite small leak

rate developed by a head of potassium chloride solution seems to be es- sential to obtain stable pH readings in some dilute, poorly buffered solutions, but "are the factors involved, as far as the junction is concerned, un- derstood? It is possible that the wide variafions of residual liquid junction

potential observed by Kater, Leonard and Matsuyama [89] are not enfirely due to the colloidal properties of blood.

Recent determinations involving carefully formed free diffusion juncfions with the necessary requirement of cylindrical symmetry have been

concerned with pH studies [45,91]. Paabo and Bates [91] have used a

cell designed by Bates, Pinching and Smith [92] to investigate the inter- nal consistency of the multistandard NBS pH scale. Alner, Greczek and

Smeeth [45] formed their junctions in a 1 mm precision-bore capillary

tube, 5 cm long, by removing the air trapped between the two solufions
REFERENCE ELECTRODES 129

V

Figure 4. Some common forms of restrained-flow junctions: a. palladium annulus, b. ceramic plug, c. J-type [100] to overcome inverse density gradient, d. cellophane membrane [89], e. ground glass sleeve, f. fiber wick in silicone rubber grommet for combination electrode. with a syringe. This size capillary gave the best results (stability to 0.04 mV over several hours); tubes of larger bore gave much poorer stability whereas narrow tubes increased the resistance of the cell and the

sensitivity of the measurement system suffered.

It is worthwhile summarizing here the evidence on which the use of a

saturated or 3.5M potassium salt bridge for reducing liquid junction

potentials is based. The first is the experimental evidence of Guggenheim

[82] from measurements on the cell Hg; Hg2Cl2|0.

1

M HClllxM KC1||0.

1

M KCliHg.Cl.; Hg

that, as X is increased, the whole cell emf falls. Since Ed is zero for this

cell, then Ed + Es is reduced by increasing the concentration of the salt bridge. Guggenheim [82] used both free diffusion and continuous mixture junctions and found for this cell that the difference in emf was not more than 0.15 mV. On this evidence rests the justification for carrying out Henderson equation calculations (based on the assumption of con-
130 ION-SELECTIVE ELECTRODES

tinuous mixing) on free diffusion junctions. Secondly, there is the

evidence based on the consideration of the Henderson equation itself [93], that for a salt bridge at high concentration when both anion and

cation have the same mobility (the ions are equitransferent), then for the

single junction, ^.g.,

Ed will vanish because of the zero pre-logarithm term. It is very important

to distinguish between this single junction case and the double junction case which appears in the cell above. In the latter, Henderson equation

considerations show that Ed will be a function of the dilute solutions principally, and not of the bridge solution. This point was made by Finkelstein

and Verdier [94] who investigated the effect of adding potassium nitrate

in different proportions to potassium chloride in order to make the ions more nearly equitransferent. The effect was to increase the whole cell potential.

A second approach to the problem of reducing liquid junction potentials, originated by Nernst, and one which is very popular, consists of ad- ding "inert" electrolyte to the solutions in the two electrode compartments so that the potential determining ions are then present in effectively

small relative concentration. The two solutions may be allowed to come

directly in contact (single junction) or a salt bridge of the same inert elec- trolyte at the same concentration is used (double junction cell). A bonus

is often additionally assumed, that if any variation in concentration of

potential determining species is made, then their activity coefficients

remain constant by the ionic strength principle. Prue and Read [95] have

recently shown from measurements on the cell

that changes in the activity coefficient of hydrochloric acid in the

presence of the inert electrolyte, sodium perchlorate, are not negligible

(Fig. 5), but can be predicted from consideration of the properties of the

electrolyte mixture in terms of parameters relating to the single electrolytes. It is certainly true that as the concentration of potential-determining species tends to zero, then Ed approaches zero, and this method

reaches its culmination in cells of the type introduced by Owen [96], e.g.,

HCl(0.1M)||KCl(sat)

Pt; H2 I HCl (mi), NaC104 fm2)|AgCl; Ag

KCl, xm AgN03,xm

Ag; AgCl KNO,. m Ag

KNO3 (1 -x)m KNO3, (l-x)m

Measurements are made at various values of x, and the emf is extrapolated to x = 0, where upon E,/=0 and E.,= (IRTlF) In yvKC kkxo:,). where
REFERENCE ELECTRODES 131

I I I I I I I I I I ai 02

m-, (mol kg~^)

Figure 5. Variation of yHcKNacio^) as a function of acid molality (mi) in sodium perchlorate

solutions (m-i) (after Prue and Read [95]): O at constant ionic strength; • at constant added salt molality. (If the ionic strength principle were correct, the lower line would

have zero slope and the upper line a negative slope if a Debye-Hiickel expression is assumed.)

yAKcKKNo.o is the activity coefficient of silver chloride present in trace amount in a potassium nitrate solution. Such extrapolations are linear,

and Spiro [97] and Covington [98] have shown that for the various

possible types of such cells, where the ionic strength is constant throughout, this is to be expected on the basis of the known properties of mixtures

of electrolytes embodied in Harned's rule and related expressions [99].

Covington [98] pointed out that in some double liquid junction cells, which are reasonably symmetrical, the two diffusion potentials (Ed)

are not equal and opposite and hence AEd 7^ 0 as is often assumed.

Clearly, more experimental and theoretical work on the design of cells with liquid junctions is desirable.

Related to Owen's method and suitable for less precise determinations,

such as the study of ionic equilibria by potentiometric techniques, is the

method employed by Biedermann and Sillen [100], in which the solution
132 ION-SELECTIVE ELECTRODES

Species of interest is added to the electrolyte on the right hand side of the

cell:

Hg; Hg2Cl2 I AM NaCl |1 3M NaClO^ (3-0.001 h) M NaC104

0.001 h M HCIO4

H2; Pt.

The electrode on the right could be, instead of the hydrogen gas electrode,

e.g., Ag+|Ag; Hg|+ | Hg; Fe^+, Fe^^ | Pt; or Ch | AgCl; Ag, with the

concentration of the potential determining species small in comparison

with the other ions present. In this cell, h is related to the x used for Owen's cell by x = h/3 or, in general, x = h//, where / is the ionic strength.

Applying Henderson's equation, it can be shown that Ea^^ (RTIF) hd/I

where d is a constant involving ionic mobilities, thus partially accounting

for the fact that plots of Ed + Es(= E - Eei) against h// are linear (Fig. 6).

100-

D

UJ

Figure 6. Variation of emf with h/I for the Biedermann-Sillen cell [100]. Upper line: O CliAgCI; Ag; • BriAgBr; Ag. Lower line: ^H + lH.; Pt; € Ag+|Ag; VFe2+, Fe^+I

Pt; X Cu2+|Cu.

Spiro [97], taking into account the variation of E.s, has shown that the

slope of the plots is in more reasonable accord with experiment. The ex-
REFERENCE ELECTRODES 133

perimental value of d can be used to make "liquid junction potential cor- rections" to titration results when h is not varied. Extensions of this work,

including attempts to take into account activity coefficient variations,

have been attempted by Sullivan and Zielen [101] and Rossotti and

Rossotti [102].

Biedermann and Sillen [100] found that the slope of the (E — Eei)

against hi I plots was different, depending on whether a cation or anion

responsive electrode was used on the right hand side of the cell above

(Fig. 6). This can be shown [103] to be a consequence of the particular

combination of mean ionic activity coefficients involved in Es for the

anion-anion electrode cell and the unsymmetrical anion-cation electrode

cell.Most of our remaining knowledge of liquid junction potentials comes

from studies of cells with junctions such as [84-86]:

HC\{0.1M)\\ KCKO.l M).

For this and similar cells with other alkali metal chlorides, data are avail- able from which Es can be evaluated, making the assumptions of a continu- ous mixture junction [84, 97]. Eg is found to be small, 0.7 mV for

HCl II KCI, but it does not follow that this will always be so. Hafemann

[104] has used a computer simulation method to calculate the potential

and its rise time for these simple junctions. His results are in agreement

with calculations by the Planck and Henderson equations and with ex- periment, if the results of Grahame and Cummings [86] are used and not those of Maclnnes and Yeh [85], whose values, in which potassium

chloride was one of the electrolytes, are incorrect. It is worth drawing at- tention to the fact that Bass [105] has reexamined and elaborated

Planck's kinetic treatment of liquid junction potentials with particular

reference to the inconsistent assumption of electroneutrality throughout

the junction, and Picknett [106] has suggested a novel method of calculating Ej which apparently does not depend on the structure of the junction.The problem of liquid junction potentials between aqueous and partially aqueous or non-aqueous solvents is an even more difficult one.

Bates, Paabo and Robinson [107] have obtained data which suggest that the liquid junction potential is constant and reproducible between aque- ous saturated potassium chloride and a given solvent mixture irrespective

of the solute buffer system, provided it is not too acid or too alkaline. It is therefore unnecessary in operational pH measurements to replace the

aqueous salt bridge by a partially aqueous one. Their 8 values [107] can

be used to correct operational pH measurements obtained with aqueous

pH standards to the appropriate pH scale for the particular solvent mixture. Gutbezahl and Grunwald [108] have calculated Ej for
134 ION-SELECTIVE ELECTRODES

ethanol-water saturated potassium chloride junctions and various buffer

solute systems in low concentration so that the Debye-Huckel limiting

equation could be used for the single ion activity coefficients. They con- cluded that Ej could be well over 100 mV for 100% ethanol. Schwabe

and Geisler [109] have recently presented results from which they claim

that Ej for such junctions is small and of the order of magnitude of aque- ous diffusion potentials. They studied, essentially, cells involving single

and double junctions of the forms:

Hg; Hg2 Ac2|NaAc(sat), CH3OH (98%)||KCl(sat), HsOjHgoCl.; Hg (I) Hg; Hg2Ac2|NaAc(sat), CH3OH (98%)||xX + (1-x) Y||KCl(sat).

H20iHg2Cl2; Hg (ID

where various proportions x of the two solvents X and Y were used in the

bridge solution which contained an acetate buffer. X and Y were water,

methanol, isopropanol, dioxane, etc., in various combinations. The measurements on cell (II) were made in two cells with hydrogen or glass elec- trodes as "bridging" electrodes (Section I.D.). The results should be the

same, and the scatter obtained (±2 mV) gives an indication of the precision of the determinations, a point not made clear in the paper [109].

They found that E^ — Ei > 20 mV for the solvent combinations in cell (II) mentioned, even when Y was phenol or toluene, substances which are immiscible with water, so that there is a sharp phase boundary at the

right hand junction in cell (II). This latter result is particularly surprising,

but Schwabe and Geisler's [109] conclusion, that the results demonstrate

that Ej in cell (I) is small, is questionable. It has been pointed out above

that in some cases [98] the residual diffusion potential in a double junction cell is the same as that in an otherwise identical single junction cell. The results are, however, extremely interesting and similar, though simpler, experiments along these lines would be valuable.

Lastly in this section, we will turn to the problem of the possibility of a

liquid junction potential caused by excessive solubility from an electrode

of the second kind in a cell without transference. Access of this dissolved

material to the other electrode must often be prevented by a closed tap or

similar means, and hence a liquid junction potential could arise. This

problem has been considered recently by Smyrl and Tobias [110] for the

cell Li|LiCl, DMSO|TlCl(5); Tl(Hg)

in connection with their suggested use [111] of the thallium

amalgam-thallous chloride electrode (Section III.F.) as a reference elec- trode in dimethylsulfoxide (DMSO). While their explanation of the divergence of their emf results from the expected values at low concentrations
REFERENCE ELECTRODES 135

of lithium chloride is correct, their arguments are erroneous. The junction

concerned is: LiCl(mi)||LiCl(wi), TlCl(m2).

Because of the absence of mobility data in DMSO, they assumed that the

three ions have equal ionic mobilities, without realizing that, if this were

so, there would be no diffusion potential {Ed), the junction then being ef- fectively homo-ionic:

LiClfmi)||LiCl(wi + m2).

Secondly, they failed to take into account that Eei will be affected by the

additional chloride molality at the right hand electrode.

A correct treatment of the problem for this cell is as follows:

The emf is E = E^-iRT/F) In = E°- (RTIF) In [m, {m, + ^2)7!] ^Ed

(RT/E) In {m'iY^-(RTIE)\n {I -\- m2lmt) + E

a

(5)

(6)

(7)

if only the ideal part of Ej is considered. The symbol y± is, with sufficient accuracy, the mean ionic activity coefficient of lithium chloride. The term

In (1 + m-zlmi) takes into account the effect of the dissolved thallous

chloride on Eei. Using Henderson's equation, where the X's are ionic conductances:

Ed = -{RTIE) In 1 +

^Xti+ ^ci mi(\u + A.ci) and since m-i < mi the logarithm can be expanded [98]

/MXti— Xci) Ea = -{RTIE)

m,(XLi + ^ci)

(8)

(9)

This can be combined with the solubility correction term to give for the

cell emf

E = E°- (RTIE) In mfyl- {RT/E) (10)

where the last term is the correction term which Smyrl and Tobias [110]

attempted to calculate. If, in the absence of experimental results, we as- sume all the mobilities are equal, then only the solubility term remains as expected. Alternatively, if as for water [112] Xci =^ -^^ti then the mobility
136 ION-SELECTIVE ELECTRODES

term is again unity and Ed = 0, but even so the mobility term is unlikely

to be very different from unity.

The values of the correction term based on the solubility correction

alone are very similar to Smyrl and Tobias' values [110], e.g., for mi =

10"^ mol kg"^ the correction is about 8 mV and for mi = 5x 10~^ mol

kg~^ the correction is about 25 mV, which agrees well with 21 mV for the experimental value at this molality. V. Temperature Effects In all precise work it is essential that a constant temperature be maintained during a series of measurements, and precautions should be taken

to see that this is so. In on-line pH measurements with glass electrodes,

it does occur, however, that the temperature of the solution of interest may vary or differ from that of the standard buffer solution. Slope factor

compensation is necessary on pH meters and "specific ion" meters in order that the pH or plon may be read directly from the meter. This is only one factor in temperature compensation, however.

It is not certain, whether ideas developed for glass electrodes and pH

meters can be applied to specific ion measurements, as this has not been

tested, but there seems to be no reason why they should not be applicable

apart from the proviso, mentioned in Section I, of the much smaller millivolt scale range involved. The use of the so-called "isopotential control"

[113,114] will be discussed in relation to pH measurements and its possible application to plon measurements follows directly.

Two distinct cases arise:

a. Both electrodes reach temperature equilibrium in the test and stan- dard buffers. Thus there are two cells involved, each at a different temperature.

b. The glass electrode reaches temperature equilibrium in both solu- tions but the reference electrode is remote and remains at a constant temperature. Thus there is a temperature gradient in the potassium chloride

solution. For the operational pH cell, we have as in Section I I.E. for a test solu- tion X:

Ex=(E°' + Ej+Ei) + {RT\n 10/F)pHx (11)

except that there is an additional term, which is the emf of the glass

electrode inner reference system, regarding the inner surface of the glass

electrode as a hydrogen electrode, viz. Ag; AgCl|HCI|H2

The difference of temperature in the measurements causes a change in the
REFERENCE ELECTRODES 137

"standard potential" term {E^' + Ej + Ei) known as a "zero shift". In general, its variation with temperature can be expressed as a power series

in temperature. However, over a limited range of temperature (20 °C) a simple linear variation is adequate, hence,

E^ = di + hT+(RT\n 10/F)pHx (12)

E will not be a function of temperature when

hT={RT\n 10/F)pH (13) or when

-b ^ F dE^

P ' RTlnlOIF /?lnl0' dr ^

'

Here, pH, is termed the isopotential [113] or the isothermenschnittpunkt

(the isothermal intersection point), since it is the pH where the lines representing the variation of Ex with pH cross. The pH at which E=0 is called the zero point or nullpunkt.

The zero shift error in terms of pH/ is [114]:

(R\n 10/F) pHi(Tx-Ts)

where Tx and Ts are the temperatures of the test and standard buffers

respectively, or as an error in pHx!

ApHx = ^^^pHi. (15)

In a pH meter with variable isopotential control, a bias potential equal

to {RT In 10/F) pH) is derived automatically to correct for zero shift. Values of pH, required for this can be derived from the temperature coefficients of the cell system, ^'.g., Ag, AgCl|HCl|H> --H2|X||KCl(sat)|Hg2Cl2; Hg

Case (b), where the reference electrode is at a constant temperature, can be treated in a similar way to obtain different pH/ values, by combining with the cell system above the thermo-cell:

Hg; Hg2Cl2|KCl(sat)||KCI(sat)|Hg2Cl2; Hg

(variable T) (fixed T)

In this case, the pH, values are independent of the reference electrode

used. The pH, value can be varied by suitable choice of the inner

reference system for the glass electrode, and symmetrical cells have special advantages [76,77,1 15].
138 ION-SELECTIVE ELECTRODES

When the data necessary to calculate pH, are not available (and this will certainly be so for ion-selective electrodes such as the fluoride electrode),

then pHj may be determined experimentally [114] using a buffer solution

whose pH values at two temperatures about 20 °C apart are known. The

pH meter is calibrated with the buffer at the lower temperature Ti and

then the pH read at Tz after enough time for the electrode(s) to temperature equilibrate, using manual or automatic slope factor compensation.

The pH value read from the meter at the second temperature T2 will differ from the true known value by

To my knowledge isopotential considerations have been applied only

to pH measurements and not even to sodium ion determinations with

glass electrodes. Even if such considerations are impractical in application to ion-selective electrodes, they do indicate the factors by which the

effect of temperature differences can be reduced. The growing tendency

among manufacturers to market their electrodes in kit form dry is greatly

to be welcomed as it gives the user much greater degree of freedom in the

design of his measuring system.

[ 1] Ives, D. J. G., and Janz, G. J., Eds., Reference Electrodes, Academic Press, New

York, 1961.

[2] Janz, G. .1., and Ives, D. J. G., Ann. N. Y. Acad. Sci. 148, 210(1 968).

[3] Butler, J. N., et al., J. Phys. Chem. 71, 910; 3294: 4479 (1967).

1 4] Feakins, D., in Hydrogen- Bonded Solvent Systems, A. K. Covington and P. .lones, Eds., Taylor and Francis, London, 1 968, p. 236.

[5] Thompson, M. R.,.l. Res. Nat. Bur. Stand. 9, 833 ( 1 932).

[6] Bottom, A. E., and Covington, A. K., Paper presented at the International Measurement Confederation (IMEKO) Symposium on Electrochemical Sensors, Veszprem, Hungary, October 1 968.

[7] Riseman,,L H., and Wall, R. A., U. S. Patent 3306837 ( 1 967).

[8] Douheret,G., Bull. Soc. Chim. Fr. 3341 (1966).

[9] Martin,.!. A., and Duperis,.!., Bull. Soc. Chim. Fr. 138(1968).

[10] Badoz-Lambling, J., Desbarres, J., and Tacussel, J., Bull. Soc. Chim. Fr. 53 (1962).

[ 1 1] Ritchie, C. D.,e/ «/.,.!. Amer. Chem. Soc. 89, 1447: 1721 (1967). [12] Frant, M. S., and Ross, J. W., Science 154, 1553 (1966).

[ I 3] Beck, W. H., Bottom, A. E., and Covington, A. K., Anal. Chem. 40, 501 (

1 968). [14] Covington, A. K., and Lilley, T. H., Phys. Chem. Glasses 8. 88 (

1 967).

[ 1 5] Shultz, M. M., Uch. Zap. Leningrad Univ., No. 169 13, 80 ( 1 953).

[ 16] Covington, A. K., Paabo, M., Robinson, R. A., and Bates, R. G., Anal. Chem. 40, 700(1968).

[ 1 7] Bates, R. G., and Alfenaar, M., N BS Technical Note, No. 453 ( 1 968). [18] Harned, H. S..and Ehlers, R. W.,.l. Amer. Chem. Soc. 54, 1350(1932).

(16)

VI. References
REFERENCE ELECTRODES 139

19] Bates, R. G.. Guggenheim. E. A.. Harned. H. S., Ives, D. .1. G.,.Ianz. G. .1., Monk,

C. B.. Prue,J. E.. Robinson, R. A., Stokes. R. H.. and Wynne-Jones. W. F. K..J. Chem. Phys. 25,361 (1956). 20] Zielen, A. J.,J. Phys. Chem. 67. 1474(1963).

21] Covington, A. K., Dobson, J. V., and Lord Wynne-Jones, Trans. Faraday Soc. 61, 2050 (1965). 22] Srinivasan, K. V.. Ph.D. Thesis. University of Newcastle upon Tyne. 1 968.

23] Bates. R. G.. Determination of pH. Wiley. New York. 1964. pp. 24-25.

24] Bates, R. G., Chapter 6, this publication. 25] Lauchlin, A. D. E..and Page, J. E., Nature 15L84(1943).

26] Gran, G., and Althin, B., Acta Chem. Scand. 4, 967 (1950). 27] Mesmer, R. E.. Anal. Chem. 40, 443 ( 1 968). 28] Durst, R. A., Anal. Chem. 40, 93 1 ( 1968). 29] Popoff.S.. Kunz. A. H..and Snow. R. D..J. Phys. Chem. 32. 1056(1928).

30] Hills. G. J., and Ives. D.J. G.,J. Chem. Soc. 305 (1951). 31] Caudle, J., Ph. D. Thesis, University of Durham. 1964.

32] Bates. R. G., Determination of pH. Wiley. New York. 1964. pp.230-245.

33] Bates. R. G., ihid., pp. 279-286.

34] Janz.G. J.,andTaniguchi. H..Chem. Rev. 53. 397 ( 1 953). 35] Janz, G. J., in Reference Electrodes. D. J. G. Ives and G. J. Janz, Eds.. Academic

Press. New York. pp. 179-230.

36] Ashby,J. H.. Crook. E. M..and Datta. S. P., Biochem. J. 56. 190(1954).

37] Manov, G. G., DeLollis. N. J., and Acree. S. F.. J. Res. Nat. Bur. Stand. 34. 1 15 (1945). 38] Pinching, G. D.,and Bates, R. G.,J. Res. Nat. Bur. Stand. 37.31 1 (1946). 39] Giintelberg, E., Studier over Electrolyt-Activiteter, G. E. C. Gads Forlag. Copenhagen, 1938. 40] GUntelberg, E., Z. physik. Chem. 123. 1 99 ( 1 926). 41] Harned, H. S., and Ehlers, R. W., J. Amer. Chem. Soc. 55, 2 179 (1933). 42] Bates, R.G., and Bower. V. E..J. Res. Nat. Bur. Stand. 53. 283 ( 1 954). 43] Covington, A. K., Dobson, J. V., and Lord Wynne-Jones, Electrochim. Acta 12, 525 (1967). 44] Guggenheim, E. A., and Turgeon, J. C. Trans. Faraday Soc. 51. 747 ( 1955). 45] Alner. D. J.. Greczek, J. J., and Smeeth. A. G.. J. Chem. Soc. . 1205 (1967). 46] Hetzer, H. B., Robinson. R. A., and Bates. R. G.. J. Phys. Chem. 66. 1423 (1962). 47] Hetzer, H. B., Robinson, R. A., and Bates, R. G., J. Phys. Chem. 68, 1929 (1964). 48] Hills. G. J., and Ives, D.J. G.,J. Chem. Soc. 311 (1951). 49] Schwabe, K., and Ziegenbalg, S., Z. Elektrochem. 62, 172 (1958). 50] Grzybowski, A. K.. J. Phys. Chem. 52. 550 ( 1 958). 51] Hills. G. J., and Ives. D. J. G.. in Reference Electrodes, D. J. G. Ives and G. J. Janz. Eds., Academic Press, New York, 1961 . pp. 1 27-162.

52] Armstrong. R. D.. Fleischmann, M., and Thirsk, H. R.. Trans. Faraday Soc. 61, 2238 (1965): see also Behr. B..and Taraskewska. J.. J. Electroanal. Chem. 19.373

(1968). 53] Dry, M. E.. and Gledhill. J. A.. Trans. Faraday Soc. 51 , 1 1 19(1955).

54] Hamer. W. J., and Acree, S. F.,J. Res. Nat. Bur. Stand. 32, 2 1 5 ( 1 944): Hamer. W.

J., Pinching, G. D., and Acree, S. F.. ihid., 35. 539 (1945): ihid. 36.47 (1946). 55] Greczek.J. J.. Thesis, University of London, 1964. 56] Shams El Din.A. M..and Kamel. L. A.. J. Electroanal. Chem. 11.111 (1966). 57] Sibbald, P. G.. and Matsuyama. G., Anal. Chem. 35. 1 7 1 8 ( 1 963). 58] Mattock. G., pH Measurement and Titration, Heywood. London. 1961. p. 153.
140 ION-SELECTIVE ELECTRODES

59] Ives, D. J. G.. and Smith. F. R., in Reference Electrodes, D. J. G. Ives and G. J. Janz, Eds., Academic Press, New York, p. 403.

Hulett, G. A., Phys. Rev. 32, 257 ( 1 9 1 1 ). Beck. W. H., Dobson, J. V., and Wynne-Jones. W. F. K., Trans. Faraday Soc. 56.

1 172 (1960). Hamer. W. J., andHarned, H. S., J. Amer. Chem. Soc. 57, 27 (1935). Covington, A. K., Dobson, J. V., and Lord Wynne-Jones, Trans. Faraday Soc. 61, 2057 (1965). Larson, W. D., and MacDougall, F. H., J. Phys. Chem. 41, 493 (1937). Larson. W. D., and Tomsicek, W. J., J. Amer. Chem. Soc. 61. 65 (1939). Larson, W. D.,J. Phys. Chem. 67, 937 ( 1 963). Larson, W. D., and Tomsicek, W. J., J. Amer. Chem. Soc. 63, 3329 ( 1 94 1 ). Covington, A. K., Talukdar, P. K., and Thirsk, H. R., Trans. Faraday Soc.60. 412

(1964). Gryzin. Yu. L. Zhur. fiz. Khim. 38. 2834 ( 1 964). Chauchard. J., and Gauthier. J.. Bull. Soc. chim. Fr. 2635 ( 1966). Schwabe. K.. and Glockner. G.. Z. physik. Chem. 59.504(1955).

Schwabe, K., Naturwissenschaften 44, 350 ( 1957). Aditya, S., Aditya, S., and Mukherjee, S. K., J. Ind. Chem. Soc. 42, 252 (1965). Bertram, J., and Bone, S. J.. Trans. Faraday Soc. 63, 4 15 ( 1967). Jena Glaswerk Schott und Gen., Mainz.. British Patent 894249( 1 962). Fricke. H. K.. Zucker 14. No. 7 (1961). Fricke. H. K.. in Beitrage zur angewandte Glasforschung, E. Schott, Ed., Wiss. Verlags mbH., Stuttgart. 1960, pp. 175-198. Hansen, M., and Anderko, K., Constitution of Binary Alloys, 2nd ed., McGraw

Hill, New York, 1958. Hu,K-H,and Scott, A. B.,J. Amer. Chem. Soc. 77. 1380(1955). Mussini.T..and Longhi, P.. Ric. Sci. Rend. A 8. 1352 (1965). Cowperthwaite. L A., La Mer, V. K., and Barksdale, J., J. Amer. Chem. Soc. 56, 544(1934).

Guggenheim, E. A., J. Amer. Chem. Soc. 52, 13 15 ( 1930); J. Phys. Chem. 36, 1758

(1930). Unmack, A., and Guggenheim, E. A., Kgl. Danske Videnskab. Selskab. Mat. Fys. Med.. No. 8. 10(1930). Guggenheim, E. A., and Unmack, A., ibid., No. 14, 10 (1931). Maclnnes, D. A.,and Yeh, Y. L.,J. Amer. Chem. Soc. 43, 2563 ( 1 92 1 ). Grahame, D. C, and Cummings, J. l.,ONRTechn. Rep. No. 5 (1950). Perley, G. A., Trans. Electrochem. Soc. 92, 497 ( 1 947). Carson, W. M.. Michelson. C. E.. and Koyama. K.,Anal. Chem. 27, 472 ( 1955). Kater, J. A. R., Leonard, J. E., and Matsuyama, G.. Ann. N. Y. Acad. Sci. 148. 54

( 1 968); British Patent 1 1 34 1 40 ( 1 968). Mattock, G., pH Measurement and Titration, Heywood, London, 1961, pp. 179-182.

Bates, R. G., and Paabo. M.. unpublished work quoted in Bates. R. G.. Determination of pH. Wiley. New York, 1964, p. 87. Bates. R. G.. Pinching, G. D., and Smith. E. R.. J. Res. Nat. Bur. Stand. 45. 418

(1950). Maclnnes, D. A., Principles of Electrochemistry, Dover, New York, 1961 . p. 244.

Finkelstein, N. P., and Verdier. E. T., Trans. Faraday Soc. 53, 1 6 1 8 ( 1 957). Prue,J. E.,and Read, A. J., J. Chem. Soc. A, 1812 (1966). Owen, B. B., J. Amer. Chem. Soc. 60, 2229 (1938).

Spiro, M., Electrochim. Acta 1 1, 569 ( 1 966).
REFERENCE ELECTRODES 14

[98] Covington, A. K.. Electrochim. Acta 1 1 . 959 ( 1 966). [99] Harned, H. S., and Robinson. R. A., Multicomponent Electrolyte Solutions. Per- gamon. Oxford, 1968.

100] Biedermann. G., and Sillen, L. G., Arkiv Kemi 5, 425 (1953). 101] Sullivan.J.C.andZielen. A.,I..J. Phys. Chem. 66. 1065 (1962). 102] Rossotti, F.J. Cand Rossotti, H., J. Phys. Chem. 68, 3773 ( 1 964). 103] Covington, A. K., unpublished data. 104] Hafemann, D. R..J. Phys. Chem. 69. 4226 ( 1965). 105] Bass, L.. Trans. Faraday Soc. 60, 1914 ( 1964); see also Guggenheim, E. A., Proc. Phys. Soc. 85.393 (1965). 106] Picknett, R. G., Trans. Faraday Soc. 64, 1059(1968).

107] Bates, R. G., Paabo, M., and Robinson. R. A.. J. Phys. Chem. 67, 1 833( 1963). 108] Gutbezahl, B., and Grunwald, E., J. Amer. Chem. Soc. 75, 565 (1953). 109] Schwabe, K., and Geisler, H., Electrochim. Acta 12, 147 (1967).

1 10] Smyrl,W. H., and Tobias. C. W.. Electrochim. Acta 13. 1581 (1968).

1 1 1] Smyrl.W. H., and Tobias, C. W.,J. Electrochem. Soc. 113,754(1966).

1 12] Robinson, R. A., and Stokes, R. H., Electrolyte Solutions, Butterworth, London, 2nd ed., 1959, p. 463.

I 13] Jackson, J., Chem. Ind. ( London) 67, 7 ( 1 948). 114] Mattock, G., pH Measurement and Titration, Heywood. London, 1961, pp. 190-197. [115] Bates, R. G., Determination of pH, Wiley, New York, 1964, pp. 327-330.

r

CHAPTER 5

THERMODYNAMIC STUDIES

James N. Butler

Tyco Laboratories, Inc. Waltham, Massachusetts 01254

I. Introduction

In this volume, we are concerned with the impact of a new technology on various aspects of chemistry. This chapter in particular is concerned

with how solid-state and liquid ion exchange membrane electrodes can be

used in studies of the thermodynamics of solutions. As is well known, the

potential of an electrochemical cell usually depends on the composition

of the electrolyte, and by a proper choice of electrodes, a cell can be made

to yield the activity of a particular component over a wide range of composition. Studies of this kind have been well documented, and range from

measurements of activity coefficients [1,2] (where the emphasis is on

relatively small deviations from the ideal behavior of a completely dis- sociated electrolyte) to studies of multiple equilibria in a constant ionic

medium [3] (where the emphasis is on strong chemical interactions and

the identification of solution species). The measurement of standard

potentials and oxidation-reduction equilibria [3,4,5] , an important part of

electrochemical thermodynamics, concerns us only peripherally in this chapter because we have limited ourselves to electrode systems of the

membrane type, which make use of ion-exchange (rather than

oxidation-reduction) equilibria.

To be somewhat general, for the moment, consider a cell of the type

"M-electrode" | M+, X", solvent, etc. \ "'X-electrode"

where the left hand electrode is reversible to the cation M+ and the right

hand electrode is reversible to the anion X". Either or both of these ions

could be polyvalent, and the "etc." which I have indicated in the electrolyte could include any number of other ions so long as the electrodes

do not respond to them. For such a cell, the potential is given by

RT

E = E^- —\n{[mnX-]yl} (1)

where R is the gas constant, T is the absolute temperature, F is the

Faraday constant, [M + ] is the concentration of the cation, [X~] is the

concentration of the anion, y± is the mean activity coefficient of the salt 143
144 ION-SELECTIVE ELECTRODES

MX in this particular electrolyte, and n is the number of electrons trans- ferred (in this case, n = \, but for polyvalent ions, n could be greater than

unity). The concentration scale is usually taken to be moles per kilogram

of solvent, but this is quite arbitrary, and might also be moles per liter of

solution or mole fraction. The standard potential E° is obtained by calibra- tion of the cell with an MX solution of known activity, and this may be

either a relatively concentrated solution for which the activity coefficients are known from other experiments, or may involve extrapolation of measurements with this particular cell to infinite dilution, where y± can be

taken equal to unity. In the above discussion, we have made a tacit assumption which is not

at all trivial; somehow we know that the electrodes are reversible to the

cation or anion specified, and to no other. How is it possible to arrive at

this conclusion? In dilute solutions, one can determine the reversibility of

the "M-electrode," for example, by keeping the concentration of X" constant and varying the concentration of M+ over a wide range. If Equation

(1) is obeyed within the accuracy that one can calculate y± from the

Debye-Hiickel theory or from other measurements (such as isopiestic

vapor pressure studies), then one can say with reasonable confidence that the "M-electrode" is reversible to the cation M+.

Of course, the restriction of electrical neutrality in the solution requires

that a second cation A+ be present to balance the charge on the anions

X-, which are not necessarily equal in concentration to M+, and this in- troduces the question of whether the "M-electrode" is specific for M+ or whether it possibly is affected by A+ also. In the usual context, "interference" implies that the cell potential varies

as if some fraction of A+ behaved as if it were M+:

£ = £° - ^In { [M-] + yc. [ A-] } - ^In { [X-] yt } (2)

where ks is called the selectivity ratio. In solutions where [A+] >> [M+]

and [X~] is constant, one expects to see a constant value of E, Such

behavior is typical of cation-sensitive glass electrodes, and kg is relatively

insensitive to solution composition [12]. However, kg may vary with both

solution composition and electrode type.

Another type of effect which may occur is that A+ forms some sort of

complexes with X", thereby diminishing the concentration of free X".

This is best treated within the framework of solution equilibria. An example is the effect of hydrogen ion on the fluoride-sensitive LaFa membrane

electrode, discussed in the next section. If A+ is in large excess, pseudo-Nernstian behavior with variations in [M+] may be observed, but

deviations will be observable in the range where [M+]/[A+] is between

0.1 and 10. If Equation (1) is obeyed in this range, then the specificity of
THERMODYNAMIC STUDIES 145

the electrode for M+ is confirmed. Unfortunately, the presence of a second

cation affects to some extent the activity coefficient y± of the salt MX,

and so unless this activity coefficient is known from some independent

experiment, a test of this type, particularly in solutions of concentration

greater than 1 molal, may be somewhat ambiguous.

With membrane electrodes and electrodes of the second kind, inter- ference phenomena may be kinetically limited and may be quite complex

inform [10].

From a discussion such as this, it becomes quite apparent that measure- ments of activity coefficients with ion-selective electrodes are intimately

bound up with the question of the reversibility of the electrodes themselves and their specificity for a particular ion. Only by amassing a considerable amount of evidence that ion-selective electrodes give the same

thermodynamic data as completely unrelated methods, can we gain confidence in measurements on new systems where there are no other data

with which to compare.

Thus there are no new principles involved in studies of solution ther- modynamics using membrane-type electrodes, but there is a new collec- tion of tools which have yet to be tested in detail to see how accurately

they can determine the quantities we desire—activity coefficients and

equilibrium constants. Before we proceed to a review of the few ther- modynamic studies which have been made with these electrodes during

their short history, let us take a somewhat broader view of the field and

see how the electrodes discussed in this volume form a logical extension

of classical measurements, and consider a number of new directions

from which to approach systems which cannot be studied by the classi- cal methods.

From the thermodynamic viewpoint, the most thoroughly studied

electrochemical cell [IJ is Pt; H2 I H+, C1-, solvent, etc. \ AgCl; Ag

which yields the mean .activity coefficient of hydrochloric acid. Measurements can be made with this cell in aqueous solutions and many

non-aqueous solutions with extraordinarily high accuracy [6,7]. Quite a wide variety of other ions can be added to the solution without interfering

with the reversibility of the electrodes to hydrogen ion and chloride ion. Examples are: alkali metal, alkaline earth, and other cations with reduction potentials more negative than hydrogen ion; sulfate, fluoride, car- bonate, acetate, and many other organic anions which are not easily

reducible or oxidizable, and which do not form strong silver complexes or

highly insoluble silver salts. The hydrogen-silver chloride cell is usually called a "cell without liquid

junction", but this is possible only because of the small amount of inter- ference between the soluble species which inevitably result from each
146 ION-SELECTIVE ELECTRODES

electrode. More rigorously, we might write the cell as Pt;HM5) I H2, H + , C1-, etc. \ H + , C1-, Ag^, AgCl, AgCk, etc. \ AgCl; Ag

a more complex notation which reflects the mechanism of the two elec- trodes as well as the materials which are dissolved in the electrolyte in contact with each electrode [5]. Only because the solubility of H2 and

AgCl in water is quite small, compared to the concentrations of HCl nor- mally studied, can the liquid junction between the two solutions be

neglected. In some non-aqueous media [7,8], the complexes of AgCl (or

analogous electrodes) are much more stable than in water, and this liquid

junction can contribute a considerable potential. In practice, no attempt

is usually made to prevent H2 from reaching the silver-silver chloride

electrode, or to prevent soluble silver species from reaching the platinum

electrode. Fortunately, the kinetics of the \\{ads) \ H+ couple and the

Ag I Ag+ couple are so rapid that small amounts of dissolved silver do not appreciably shift the potential of the hydrogen electrode, and small

amounts of dissolved hydrogen do not appreciably shift the potential of

the silver electrode.

An analysis of the type we have just gone through can be made only

when the mechanism of each electrode reaction as well as all the possible

equilibria and transport phenomena within the electrolyte are quantitatively understood. With such a complete mechanistic understanding, we

can predict not only what conditions (extremely dilute or extremely con- centrated HCl, oxygen present in the solution, etc.) can interfere with the

operation of the electrodes, but we can also predict quantitatively the extent to which various ions added to the solution can interfere with the

specificity of the electrodes.

Equilibria have also been studied with this type of cell. If the concentration of chloride ion is fixed, then the hydrogen electrode responds to changes in the activity of hydrogen ion, and equilibrium constants for

various acid-base reactions can be measured quite accurately, either in a medium of constant ionic strength, or in a series of media which allow ex- trapolation to infinite dilution. The versatility of the hydrogen-silver chloride cell results from the high

degree of specificity of the two electrodes used; and this cell has been ex- ploited for a large variety of thermodynamic measurements. However,

many substances interfere with its operation, particularly ammonia, cyanide, or thiosulfate, which convert AgCl to stable, soluble complexes;

bromide, iodide, or sulfide, which convert AgCl to a less soluble salt; any

organic or inorganic material reducible by hydrogen at a platinum elec- trode, or oxidizable by hydrogen ion or silver ion at either a platinum or

silver electrode — which excludes a great many materials of interest to the biochemist, biologist, organic chemist, and analytical chemist.
THERMODYNAMIC STUDIES 147

Furthermore, it can measure only the mean activity of HCl in an electrolyte, and attempts to extend this kind of cell to other salts did not yield

nearly such a wide variety of information.

The problem faced by the electrochemical thermodynamicist who had

only a few classical electrodes at his disposal was quite clear: there were many systems for which he would like to have thermodynamic data which were quite inaccessible by means of any electrochemical cell he could

devise. For example, measurement of the activity of ZnCU in the

presence of NaCl was simple and could be carried out with the cell Zn(Hg) I ZnCl,, NaCl, H.O | AgCl;Ag

On the other hand, there was no way in which a cell could be set up which

measured the activity of NaCl in the presence of ZnCl2, until the advent

of cation-sensitive glass electrodes.

One of the very important techniques for studying complex equilibria

is to use a constant ionic medium consisting of a high concentration of

inert salt {e.g., NaC104) which keeps activity coefficients and liquid junction potentials constant provided the other ions (of interest) are at rela- tively low concentrations. Even though the constant ionic medium

technique could have been applied to some studies of complex equilibria as early as 1900, it was not employed widely until the Debye-HUckel

theory and studies of ion-pairing phenomena had made it clear that there were electrolytes which were relatively inert toward interaction with

many ions, and which could be used to keep the activity coefficients constant while the equilibria were unraveled.

The development of the proton-sensitive glass electrode and its widespread adoption for the measurement of pH was the first really sig- nificant use of a membrane-type electrode for thermodynamic measurements. Even so, for a long time glass electrodes were mistrusted by ther- modynamicists, because their potentials drifted with time and could not be referred to a primary standard redox couple. One of the first studies to make extensive use of glass electrodes for thermodynamic measurements was the work of Bjerrum [9] on the complexes of metal ions with ammonia. By using a constant ionic strength medium consisting of an am- monium salt, changes in glass electrode potential could be made to reflect changes in NH3 concentration. The long succession of studies by Sillen and coworkers [3] of hydrolytic equilibria, and of Schwarzenbach and

others on the formation of complexes between organic compounds and

metal ions [3] has exploited both the constant ionic medium concept, and

the measurement of hydrogen ion activity with a glass electrode to deter- mine indirectly the activity of an acid or base which is the complexing

ligand. Although initially there was a strong prejudice in favor of

acid-base equilibrium constants measured in the hydrogen-silver chloride
148 ION-SELECTIVE ELECTRODES

cell, within recent years many accurate studies have been made with glass

electrodes [5,1 1]. The development of special glasses which could be used to make elec- trodes reversible to alkali metal cations gave a new dimension to ther- modynamic studies [12]. Measuring the activity of NaCl in the presence

of ZnCb, which we mentioned before as being impossible for the classical electrochemist, now became simple with a cation-sensitive glass electrode

which showed highly specific response to Na+ and essentially no

response to divalent ions such as Zn++. These cation-sensitive electrodes

are now sufficiently stable, and the associated electronic measuring in- struments sufficiently sensitive and noise-free that measurements have

been made of the activity coefficients of, e.g., NaCl either alone [13,14] or in the presence of other electrolytes [15,16] which rival in accuracy

the classical measurements using amalgam electrodes or the isopiestic

vapor pressure method [6]. An important prerequisite for these accurate measurements is the availability of standard solutions in which the activi- ty of NaCl is accurately known. This problem of establishing standards is a general one, and is discussed in detail in Chapter 6. Finally, we come to the development of membrane electrodes made

from materials other than glass, which are the subject of this volume. The

origin, mechanism of operation [10,12] and uses of these electrodes are discussed in other chapters, and the remainder of this paper will be

devoted to a review of their use in thermodynamic studies. Lest we lose perspective, however, let me summarize this introduction by saying

again that these electrodes provide us with new tools for thermodynamic

studies, but that these tools must be themselves thoroughly studied and

their results compared with all other available methods, before we can

trust them as we have learned to trust the classical and glass electrodes

before them.

II. The Lanthanum Fluoride Electrode

Without doubt, the most unusual and probably the most significant of

the solid-state membrane electrodes is the lanthanum fluoride electrode.

First announced in 1966 by its inventors, Frant and Ross [17], it was of

such immediate interest that by the end of 1968, more than 25 papers con- cerned with this electrode had appeared in print.

The unique property of a europium-doped lanthanum fluoride crystal

to form a membrane apparently permeable to fluoride ion and virtually no other anion or cation, provided the first fluoride-reversible elec- trode, and indeed one of the few truly specific ion-selective electrodes.

As we will see in detail below, this electrode gives Nernstian response

to fluoride ion concentrations from above \M to below IQ- W, and only

OH" seems to interfere with this response.
THERMODYNAMIC STUDIES 149

Essentially all the studies discussed in this section have been performed

using the cell Hg;Hg2Cl2(5) I KCl(sat) II F-,^/c. | LaF3(5) | NaF(0. IM), NaCl

{0AM) I AgClf5j;Ag

The left hand half cell is a commercial saturated calomel electrode, and

the right hand half cell is contained within the plastic body of the commercial (Orion Research, Inc.) "fluoride electrode." If the LaFa membrane is permeable only to fluoride ion, the potential of the cell should be given by

E=EAgcuAg - EscE - ^ In [F-]yF + ^« + (3) r Here Ea is the asymmetry potential of the membrane, and Ej is the liquid

junction potential between saturated KCl solution and the test solution.

Both these terms are usually combined with the potential of the internal

silver-silver chloride electrode and the calomel reference electrode, and

are found to be relatively constant with time and relatively independent

of the test solution composition:

E=E- ln[F-]7p

(4) E°' is now a constant which is determined by calibration in a solution of

known fluoride ion activity.

The use of a single ion activity coefficient introduces some ambiguity

in relatively concentrated solutions, and for rigorous measurements, a cell without liquid junction, where the other electrode is reversible to a cation

in the test solution, should be used. However, no such measurements

have been published, although we will discuss below some work which is presently in progress. For solutions more dilute than O.IM, however,

is usually taken to be equal to the mean activity coefficient y± of NaF in a solution of the same ionic strength. Alternatively, yp may be calculated from some variant of the extended Debye-Huckel theory. For concentrations below 0AM, the error is of the same order of magnitude as the

experimental measurement errors. At higher concentrations, the ambiguity becomes important. In a constant ionic medium, the actual value of the

activity coefficient need not be known, since it is constant throughout the

various experiments and can be included in the standard potential, E°'

,

when calibrations are made.

A. Selectivity

A number of studies have borne out the initial optimism about the

unusual selectivity of this electrode. In their initial communication, Frant and Ross [17] stated that "Adding 0AM NaCl or NaNOa to a solution
150 ION-SELECTIVE ELECTRODES

containing IQ-W fluoride ion results in a 7 mV decrease in potential . . and that IM Cl~ or NO3" results in a 20 mV decrease in potential. These changes are approximately what would be expected from

the change in ionic strength resulting from the addition of the other salt. Although no data were available from which to predict the effect of NaCl

or NaNOa on either the mean activity coefficient of NaF or on the liquid

junction potential of the solution with saturated KCl, estimations based on the Debye-Huckel theory and on the activity coefficient of pure NaF

solutions at concentrations from 0.1 to l.OM agreed within approximately

10% with the observed values. In the presence of 0. IMSOr the

potential of the electrode in lO-^M fluoride was observed to shift by

13 mV instead of the predicted 18 mV, but this is certainly within the

possible error in estimating the activity coefficient of F- in the presence

of a divalent "instead of a monovalent ion. Bicarbonate, phosphate (pH =

6.4) and acetate (pH = 4.9) apparently do not cause any interference

either [18].

Although we will discuss deviations from the Nernst equation in more

detail below, it is worth noting now that approximately the same (Nernstian) slope of the calibration curve (Fig. 1) is obtained in O.IM KNO3

[19], l.OM NaCl [20], or O.IM MgS04 [20] containing various amounts

of KF or NaF as in solutions containing KF or NaF alone. This result confirms the lack of interference by K+, Na+, Mg+ +

, NO:7,Cl-, and SOf

.

Deviations in Figure 1 at the \0~^M fluoride concentration are due at least in part to ionic strength changes.

Looking at the same type of measurement from another perspective, we

have listed in Table 1 the response observed for a lanthanum fluoride

electrode {vs. SCE) to 1 0-W NaF in a buffer consisting of 0. 1 8M sodium

potassium tartrate, 0.0 12M disodium citrate and 0.008M NaOH to which

various substances were added [20]. In all cases, the pH was between 5.0

and 6.3, where there is expected to be no interference by OH- or from the

formation of protonated fluoride species (see below). The citrate and tar- trate tend to complex transition metal ions, and thus to minimize any ef- fects from the formation of complexes of these ions with fluoride. An interfering ion would be expected to make the potential of the

fluoride electrode more negative, and only in the silicate solution was this observed. There, the shift was only 0.3 mV for a 65-fold excess of sil- icate over fluoride, and can probably be attributed to fluoride impurities

in the silicate. Other explanations may be a shift of the liquid junction

potential, or possibly the formation of a slightly charged film of

silicate-based material on the surface of the lanthanum fluoride membrane. This latter possibility is suggested because the potential becomes

5 mV more positive when the pH is changed from 7 to 4, when silicate

is present, but not in solutions containing fluoride only.
THERMODYNAMIC STUDIES 151

Figure 1. Potential of LaF:i membrane electrode as a function of fluoride concentration

in various supporting electrolytes. Note that the zero of the potential scale depends on

the internal filling solution and is different for data from References 19 and 20. For all the other additions listed in Table 1 , the potential becomes more

positive, which is consistent with the formation of fluoride-containing

complexes with the added ions. The shifts in the presence of 0. IM NaCl,
152 ION-SELECTIVE ELECTRODES

Table 1= Potential of lanthanum fluoride membrane electrode.

Added substance Concentration (M) pH E (mV)

None 5.9 + 68.2

NaCl'^ 0.1 5.9 68.9

MgS04 ^ 0.01 5.8 69.0

I^e2(S04)3 + NaOH 0.01 5.4 69.0

NH4A1(S04)2 - NaOH 0.01 5.2 131.0

H3BO3 0.1 6.3 70.0

u.uudo o.y BeS04 + NaOH 0.01 5.7 100.4

ZrOCl2 + NaOH 0.01 6.2 93.2

TiOS04 0.01 ) 6.2 69.4

Na2S04 0.1 )

^vs. SCE at 23 °C. Solutions contain, besides the substances listed,

10"^ M NaF, 0.18 M sodium potassium tartrate, 0.012 M disodium

citrate and 0.008 M NaOH. From Ref. 20.

^ See also Figures 1 and 9.

0.0 IM MgS04, O.IM H3BO3, and titanyl sulfate probably reflect simply

the changes in ionic strength, but weak complexes of fluoride with Mg++

are possible (see below). Iron(III) is complexed by the buffer solution,

and the iron fluoride complexes are apparently too weak to result in any

appreciable shift in potential. Aluminum, on the other hand, is strongly

complexed by fluoride, as is beryllium and zirconium. Additions of these

metallic ions result in a substantial positive shift in potential. More

detailed studies of complex formation equilibria will be discussed later. Only small shifts in potential [20] resulted from the addition of large

concentrations of some non-ionic materials to \0~^M NaF solutions, as can be seen in Table 2. These shifts can probably be accounted for by

changes in the activity coefficient of NaF due to the salting-out effect. It

is particularly worthy of note that hydrogen peroxide has the effect of
THERMODYNAMIC STUDIES 153

making the potential more positive, which might indicate the formation of

weak complexes between fluoride ions and the protons of H2O2.

Table 2. Influence of non—ionic compounds on the lanthanum

fluoride electrode.^

rVLlQlLl Vfc; AEL—1 1 J (mV) \ 111 T / None 0

Glucose 0.1 -1.1

1.0 -0.4

Urea 0.1 -0.5

1.0 -4.0

H2O2 0.1 + 0.7

1.0 + 4.0

^ Data from Ref. 20. Measurements vs. SCE at 23

All solutions 10~^ M in NaF.

Baumann [21] showed that the slope of a curve of potential versus log

NaF concentration had the same slope (59 mV) in 1, 5, and lOM

phosphoric acid as in water alone, although the potentials shifted to more

positive values as the acid concentration increased, because of the formation of protonated fluoride species. In lOM phosphoric acid, Fe(III),

Al(III), or Th(IV) showed only a slight effect on the potential,

because they were complexed by the phosphoric acid and were not availa- ble to complex with fluoride ion (which was, of course, also highly complexed with H+). In this same study, negligible interference was found for N03~,C1", and phosphoric acid at the \M level, even though the

fluoride level was as small as lO-'^M. It was also pointed out that sodium

silicate (IM, neutralized with phosphoric acid) contains small amounts of

fluoride (7 x 10"^ in the sample analyzed), which tends to confirm that the negative shift in potential in the presence of silicate (Table 1) resulted

from fluoride impurity.

The most extensive test of the specificity of the electrode for fluoride

in the presence of chloride was made by Mesmer [22]. Fluoride response was Nernstian in the presence of 1.00m chloride to below 10~^m fluoride;
154 ION-SELECTIVE ELECTRODES

and when the different NaCl or KCl samples were corrected for an as- sumed fluoride impurity {SxlO'^M to 6xlO-^M), then Nernst behavior was obtained to below \0~^M, in agreement with results obtained in pure NaF solutions. These data emphasize the importance of

using salts of ultra-high purity when doing experiments in a constant ionic

medium.

Addition of HCl to a l.OOm NaCl solution, in which the fluoride content was estimated (from deviation of the Nernst plot for added fluoride)

to be 5.6 X 10~^m, gave potentials which corresponded well to those cal- culated from the dissociation constant for HF obtained by other methods

(see below), confirming that the deviation was indeed due to a fluoride impurity and not to a chloride interference. Additional confirmation was obtained by adding Be++, which decreased the measured free fluoride concentration. The upper limit for chloride interference was placed at < 2 X

lO-^m in the presence of 1.00m chloride. The selectivity of this electrode

is thus extraordinarily good.

A similar conclusion was reached by Gatewood [23] who showed that the fluoride response in 12.5% HCl solutions (3.64M) was Nernstian

(±5 mV) to below lO^W fluoride concentrations.

B. Stability and Kinetic Response

Because glass pH and cation-sensitive electrodes are known to drift in potential over long periods of time, it is of interest to inquire whether the

lanthanum fluoride membrane electrode is subject to similar difficulties. The published evidence is not entirely consistent. Lingane [18] stated

that the constant E° in the equation

E=E''-^ ln[F-]yp (5) was constant within ± 1 mV for several weeks. Durst and Taylor [19]

made measurements over a 1-week period on samples of their solutions

and noted that the potential underwent only random variation during

that time. In solutions of concentration lO^^M or greater, the 95% confidence limits on the mean of 2 1 measurements (3 each day for 7 days) were

±0.5 mV. Reproducibility on a given day was "only slightly better than

that between days. . . . The long term deviation . . . was found to be

random (bidirectional) and approximately 2 mV/week." Part of this variation was attributed to temperature changes, and to the variability of

the liquid junction potential with the SCE reference.

Srinivasan and Rechnitz [27] noted that stirring sometimes had a substantial effect on the observed potential. In lO-^M NaF solution, the

potential changed from — 61.5mV in a quiescent solution to —55.5

mV in a rapidly stirred solution. This shift was less at high concen-
THERMODYNAMIC STUDIES 155

trations, and negligible in the presence of \M NaNOs supporting electrolyte, even at fluoride concentrations as low as 5xlO-'^M. They

recommended that readings be taken with slow stirring (by a Teflon-coated magnetic bar), and that under these conditions reproducibility was excellent: 'The potentials were found to be quite stable, changing not more than 0.1 mV even after an hour. The reproducibility on the same day for two different solutions of the same concentration was within

0. ImV." In contrast to Durst and Taylor's results, Srinivasan and

Rechnitz observed a monotonic change in potential with time: "After a period of 2 weeks, the electrode gave a reading 3 mV more negative, and

after a month, 7 mV more negative for the same solution. The slope of

the calibration curve was found to be unchanged."

Even more rapid drifts in potential have been observed. Although

reproducibility was on the order of ±0.2 mV, a shift of E° by 1.8 mV

in 1 or 2 days has been observed [26]. Thus, it seems to be essential to calibrate the electrode at least every day and perhaps'between each measurement if very precise results are desired. However, the rate of drift does not seem to be large enough to warrant continuous recording of the

potential and extrapolation of measurements made in test and reference

solutions to the same point in time, as is often done with glass electrodes

[13-16,28].

The kinetic response of the electrode is "almost instantaneous"

[27,29], limited by the recorder response time of 0.5 sec, at least in solutions containing fluoride concentrations greater than millimolar. In very

dilute solutions, the response time has been reported to be very long. In a 10-W NaF solution, for example, a steady potential was reached only

after approximately 1 hour [20]. This may have resulted from small

amounts of more concentrated solution which accumulated in crevices near the edge of the LaFs crystal, and conceivably does not reflect the

true response of the membrane. It has been reported that some pieces of

the first model of the electrode produced (Orion Model 94-09 with a white

plasfic body) "had an interstice between the crystal and the body of the

electrode. Slow diffusion of the test solution into the interstice was

responsible for the slow rate at which the system came to equilibrium.

The . . . new model . . . has its crystal cemented into the body to eliminate the interstice. . . . Equilibrium is attained in less than 3 minutes at 10-«M fluoride concentration. The response is more rapid at higher concentrations" [30]. The ultimate response speed of the elec- trode has not yet been determined but may be diffusion controlled, and

with rapid-mixing systems, kinetic studies in the millisecond range may be

possible.

348-381 0-69— 12
156 ION-SELECTIVE ELECTRODES

C. Acidity Effects

In their original communication, Frant and Ross [17] pointed out that there were changes in potential as the pH of fluoride solutions was

changed. A diagram illustrating this effect is presented in Figure 2 [20].

Figure 2. Effect of pH on the potential of the LaFa membrane electrode in NaF solutions of various concentrations. Data from Reference 20. Since that time, it has been well established that the positive shift in potential observed in acid solutions is due entirely to protonation of the

fluoride ion, and that neither HF nor HF^ produces any interference.
THERMODYNAMIC STUDIES 157

The electrode obeys the Nernst equation (in terms of free fluoride ion activity) precisely in this region [27]. More details will be given below in a

discussion of the HF equilibria.

The negative shift in potential in basic solutions is not so well un- derstood. Frant and Ross [17] stated: "The only significant interference comes from hydroxide ion, which is not surprising in view of the similarities in charge and ionic radii. In pure solutions, significant hydroxide in- terference occurs when the concentration of hydroxide about equals the

concentration of fluoride, and a tenfold excess of hydroxide will double

the apparent fluoride content." This implies an interference of the simple

additive type:

but ks, the selectivity ratio, is not approximately 0.1, independent of

fluoride concentration (as stated above), but varies from essentially zero

in 10-W fluoride to greater than one in \0-^M fluoride. Furthermore, the

approach to a steady potential value has been reported [20] to be much

slower in basic solutions. This is shown in Figure 2. At pH = 12 it takes

as long as 3 hours to reach a steady potential in 10-^M fluoride solution.

Curiously, the interference is greater at short times than it is at steady

state. The mechanism of the hydroxide interference is still unexplored. Frant

and Ross [17] implied that hydroxide ions took the place of fluoride ions

in the LaFs crystal lattice because of their similarity of ionic radii. Bock

and Strecker [20] made no hypotheses to explain the deviations at high

pH values.

It is of interest to examine the possibility of the equilibrium formation

of a lanthanum hydroxide complex or precipitate, which might set free fluoride ions, which could then cause a potential deviation in the direction

observed; for example:

The solubility product, K's,, for La(OH)3 is approximately 10-^^^ [3]. Although for freshly precipitated LaFu, the solubility product, Ksp,^ is ap- proximately 10^8 [24], the effective solubility product of the LaFs elec- trode crystal even in unstirred solutions is on the order of 10-^2, as we

discuss below in connection with deviations from the Nernst equation at low concentrations. Thus the equilibrium represented by Equation (7) predicts that LaFa will dissolve to produce La(OH)3 whenever

E = E°- ^ ln{[F-]+/:.[OH-]}

t

(6)

LaF.sf5j + 3 0H- ^ La(OH)3f5j + 3 F- (7)

(8)

K^p, is equivalent to the lUPAC notation for the solubility product constant A^.,o.
158 ION-SELECTIVE ELECTRODES

Depending on which value is chosen for Kgp, this ratio can be between

0.05 and 1 .0. Note that this is close to the range of the observed ratios for which hydroxide interference is observed (Fig. 2). The mechanism can be more complicated, however, since at high pH

values, stable lanthanum hydroxide complexes are formed in solution [3].

At pH = 11, for example, the predominant species in equilibrium with

La(OH)3 is LaOH + + , with a concentration of lO-^^-^M. Smaller concentrations of La^3 (lO-i^W) and La2(OH)t^ (lO-i^W) are also present. Thus, even if solid La(OH)3 did not precipitate, high pH solu- tions would tend to lower the concentration of free La+^ and, if this was in equilibrium with the LaFs crystal, liberate excess F~ into the boundary

layer region near the electrode. Since F~ would be continually removed

from the electrode by stirring or diffusion under normal measurement

conditions, but would build up in solution, one would predict that the

potential would show a long-term drift to more negative values and that

this drift would be faster with small solution volumes. However, the only

time dependence data available (Fig. 2) show that the potential drifts in the opposite direction, to more positive potentials.

Studies of this phenomenon would probably be most clearly defined if a very small {i.e., 50 /itl) sample were used in the type of setup described

by Durst and Taylor [19]. If care were taken to avoid convection, the

kinetics of the hydroxide interference could possibly be interpreted using

linear diffusion theory, and the mechanism could be elucidated.

Radiotracer studies of lanthanum concentration, though difficult, might

also be feasible, since the half-lives of the slowest-decaying radioactive

isotopes of lanthanum are of the order of a few days.

D. Deviations from the Nernst Equation

The most rigorous test of the Nernst equation would be best made in a

cell without liquid junction, but such measurements have not yet been

published. In our discussion of acfivity coefficients, below, we present some unpublished measurements made over a limited range of composition, in a cell without liquid juncdon, which apparently confirm the

Nernst equation within the precision of the measurements. In this secfion,

however, we will examine measurements made with the cell with liquid

junction

Hg; Hg>C\2{s) I KCl (sat) || F", etc. \ LaF, membrane electrode

both in solutions containing NaF or KF alone, and in various constant

ionic media.

Quite a number of workers have verified that deviations from the

Nernst equation are less than 1 or 2 mV in the range from 0. IM to below
THERMODYNAMIC STUDIES 159

lO-^M [18,19,20,22], but the ultimate precision of measurement is considerably better than this, and some of the uncertainty arises because of

the presence of a liquid junction (between saturated KCl and the test solution) of variable potential. Results obtained in a constant ionic medium

are more likely to be free of liquid junction errors than results in a medium

of varying ionic strength.

The potential of the LaFa-SCE cell is expected to obey a Nernst equation of the form:

and it is important to recognize that yp and Ej cannot be measured independently. In a constant ionic medium, both and Ej are virtually constant and can be included in E°; but in a medium of varying composition, both can be expected to vary. Making measurements in a cell without liquid junction avoids this thermodynamic uncertainty, but most

investigators have chosen to calculate according to some assumption,

and thus to lump whatever additional deviations occur from the Nernst

equation into Ej. Conversely, one may calculate Ej (e.g., by the

Lewis-Sargent equation [5]) and lump additional deviations from the

Nernst equation into the single ion activity coefficient. Uncertainties in the activity coefficient of fluoride ion and the liquid

junction potential are expected to be of most concern at high concentrations. At low concentrations, two additional problems arise: the presence

of fluoride impurities in the salt used to prepare the constant ionic medium (if one is used) and fluoride contributed by the intrinsic solubility of

LaFs in the test solution. These contributions may be expressed as follows:

where Cp is the concentration (moles/liter) of fluoride deliberately added

to the test solution, Cp is the (unknown) concentration of fluoride impurity in the supporting electrolyte, and A^sp is the solubility product of LaFa. To see deviations from the Nernst equation quantitatively, the best

published data are those of Durst and Taylor [19], for which a statistical estimate of the error in potential at each concentration was made. In Figure 3 we have plotted values of the function

E=E°-^\n[F-]y,^Ej (9)

[F-]=Cp+c;+ (10)

In Cpyp (11)

calculated from the data of Durst and Taylor. If liquid junction potentials are constant, this function should approach E° at high concentrations. For
160 ION-SELECTIVE ELECTRODES

these calculations yp was assumed to be equal to the mean activity coeffi- cient of NaF at the same ionic strength. (Unfortunately, the ionic strength was not precisely constant, but varied between 0.1 and 0.2 in the high

concentration range, because the concentration of NaF was varied and

the concentration of KNO3 supporting electrolyte was kept constant at O.lM.j

Figure 3. Deviations from the Nernst equation according to various assumptions which

are described in the text. Data from Reference 19. For Cp ^ 10"'', E' is constant within the experimental error (95% confidence limits, 21 measurements) calculated by Durst and Taylor. At

10-W and below, however, the deviations in E' are in the direction pre- dicted above and are well outside the experimental error. To test whether

these deviations are due to a fluoride impurity in the supporting elec- trolyte we have also plotted in Figure 3 the function

F' = £ + ^ln{(Cp +Cp)yp}

r with Cp chosen to be 2.5 x lO W. This amounts to only 25 parts per

million of fluoride in the KNO3 supporting electrolyte, and is not un- reasonable. The precise value of Cp was chosen to make the calculated

value of E" at lO^W equal to the best estimate of E°. It turns out that
THERMODYNAMIC STUDIES 161

this also causes the E" value at 5 X IQ-^M to be equal to E°, an excellent

confirmation of the assumption.

Still, there are deviations of E" to more negative potentials, at IQ-W,

which could be due to the intrinsic solubility of LaFs, even though the ex- perimental error is large enough to account for such a deviation. If this deviation were due to fluoride from the LaFs crystal, the effective solubility product could not be greater than K^^ 10~23. This observation is interesting since the value of K^^ measured by Lingane [24] by titration of fluoride with lanthanum nitrate, in a solution of

ionic strength approximately 0.08M, was lO-^^-^. This much larger value

is entirely inconsistent with the data of Figure 3. Durst and Taylor used

a sample of only 50 /xl, and one would expect that this small volume of

solution would be more likely to have reached equilibrium with the LaFs

crystal. The alternative hypothesis that Cp = 0 and that all deviations of E' from constancy are due to the solubility product does not give good in- ternal consistency at all. The value of A^sp obtained varies from IQ-^o s (fitting the 10-W point) to 10-22-2 (fitting the lO-W point).

Furthermore, the data of Frant and Ross [17], obtained in KF solu- tions without supporting electrolyte, and the data of Lingane [18], obtained in 0.1 OOM NaNOs supporting electrolyte, tend to support the

value of A^sp which we obtained from the deviations oiE" . Here there is no question that Cp is small, since there is no foreign salt present which

could carry fluoride impurities. The curve given by Frant and Ross is consistent with a solubility product A^sp^ 10- 24 5^ jj^ agreement with the result obtained from Figure 3. (Frant and Ross [17] gave the value A^sp^ 10-2^,

but this implies that the free fluoride concentration in a saturated LaFs

solution is approximately 10-W. From the curves displayed by both

Frant and Ross [17] and Lingane [ 18] , the free fluoride concentration is much closer to 10-W.)

Turning now to the high-concentration region, we see from Figure 3 that the point at 10-W deviates slightly from the best estimate of E°. Although we have attempted to compensate for the fact that the ionic

strength for this point was twice what it was in dilute solutions (by using a value of jy corresponding to 0.2M NaF instead of 0. IM NaF), and the

deviation is within the 95% confidence limits for the measurements, it is worth pointing out that this magnitude of deviation corresponds to a 10%

error in estimating the activity coefficient, in the direction of a larger activity for fluoride ion than that predicted purely from ionic strength considerations. Alternatively, a shift in liquid junction potential (because the

test solution changed in composition from essentially 0. IM KNOs to O.IM KNOs-O.lM NaF) of 0.5 mV could also account for the deviation. From our measurements of the activity coefficient of NaF in NaF-NaCl electrolytes (see below), one would expect that the mean ac-
162 ION-SELECTIVE ELECTRODES

tivity coefficient of NaF in NaF-KNOa electrolytes could be somewhat

larger than in NaF at the same ionic strength. This is in agreement with

the deviations in Figure 3. More recent work [26], using a constant ionic medium of high concentration in a cell where the liquid junction potential is almost certainly

negligible, has confirmed the Nernstian behavior of the LaFs electrode.

The cell used was

Ag; AgCl I KCl (3M) 1

1 K+, F", Ch | LaF, membrane electrode

where the concentration of KF and KCl in the right-hand compartment

were varied, but their total concentration was kept at 3M. This assured

that both the liquid junction potential and the activity coefficient of

fluoride ion were kept constant (so long as the concentration of KCl was much greater than the concentration of KF). Under these conditions, the

activity coefficient and liquid junction potentials are lumped with the

standard potential. Figure 4 shows how the quantity = E + 59.16 log Cp (13)

varies from 0.00 IM to 0.2M fluoride. The 95% confidence limits on E°'

are ±0.5 mV, in agreement with the results of Durst and Taylor [19] in the range from 10-^ to lO-W.

Figure 4. Deviations from the Nernst equation in 3M KCl solutions, including any variation of activity coefficients or liquid junction potential. Data from Reference 26.
THERMODYNAMIC STUDIES 163

We may thus conclude from these studies that the Nernst equation is obeyed well within experimental error for all fluoride concentrations

above lO'^M, and that any deviations in that region in the direction of

negative potentials can probably be explained in terms of fluoride impurities. The effective solubility product of the LaFs crystal appears to be ap- proximately 10~24, which is in marked disagreement with the value of

10-^*^ obtained from freshly precipitated LaF.?, as described in the next

section. A possible explanation for this discrepancy is that the freshly

precipitated material is a hydrated form of considerably higher free ener- gy than the massive crystal used to construct the electrode.

Deviations from the Nernst equation in the direction of more positive

potentials are almost certainly due to the formation of complexes between

fluoride and one of the other ions in the solution. Such phenomena are best treated within the framework of solution equilibria, and are discussed

in detail in the next section. E. Equilibria

The most important equilibria which the fluoride ion engages in are those with the hydrogen ion, and these have been the subject of considerable study before the advent of the LaFs membrane electrode [3].

However, this new electrode makes possible a new experimental ap- proach, and since the analysis of the data obtained is typical of all equilibrium studies in constant ionic medium, we shall present the results

in some detail. Further discussion of the approach used can be found in standard reference works [9,32,33].

As discussed above, in a constant ionic medium, the potential of a LaFs

membrane electrode with respect to a reference electrode (e.g., SCE) is given by the free fluoride concentration:

E = E°-^\n[F-] (14) F

The standard potential E° is obtained by calibration in solutions containing NaF at pH values {e.g., 5-7) where there is negligible protonation of

fluoride. Then acid is added and the potential observed. For a complete

study, the total fluoride concentration is changed by several orders of

magnitude to test for polynuclear complexes (e.g., H4F.t [34]). From

the materials put into the solution, the total concentration of fluoride, Cp,

and hydrogen ion, Ch, are known, and the most popular function to use in analyzing the data is the ligand number

(15)
164 ION-SELECTIVE ELECTRODES

This is the ratio of bound fluoride to total hydrogen. If HF were the only

complex formed, n would vary between 0 and 1. The data of Figure 5

[27] show clearly that n exceeds unity at high fluoride concentration,

and thus that species such as HF2 are important. The fact that all points

fall on the same curve is evidence for the mononuclear (i.e., HF„) nature of the complexes, since the total fluoride concentration [27] was varied over the range from 0.00 IM to 0.5 M. The ionic strength was kept constant at 1 .OM with NaNOs for these measurements.

0.5

log [F"] Figure 5. Bjerrum plot of experimental values for ligand number n as a function of free fluoride ion concentration. Note that n exceeds unity at high fluoride ion concentrations; a direct confirmation of the existence of complexes other than HF. Data from Reference

27.Assuming the equilibria:

H+ + F-^HF (16)

HF + F-^=^HF2- Kz (17)

the ligand number may be expressed as

. /3.[F-]+2/32[F-]-^

J. l+/3,[F-]+^.[F-]2 ^

^
THERMODYNAMIC STUDIES 165

where (3ii=Ki) and /32(=A^iA^2) are overall formation constants. This

expression can be cast into a linear form [32,33j:

(l-.)[F-].103 = ^' • 10"'+^^ • 10"(t^3 . 103 (,9)

which is of the form

y^a + bx (20)

with a = 10-3 and b = 10"^ ^82. The functions y and x are easily calculated from the experimental data of Figure 5, and are displayed in Figure

6. Note that x-» 00 at n = 1 , and thus the value of fS-z is heavily weighted by

-300 -200 -100 0 +100 +200 +300 +400 +500 +600 +700 +800

X Figure 6. Linear plot to determine equilibrium constants for the formation of HF and

HF2" as described in the text. Data from Reference 27. points in that region. On Figure 6, two slopes have been indicated, and a "best value" is p2 = 10^-^^. This slope has been used to draw the curve of

Figure 7, which is an enlargement of the region of low jc, and the intercept

corresponds to ^8, = 10^ 89. An independent study by Neumann and Sillen [26] has given the

results which are partially shown in Figure 8. An analysis using considerably more data and the least squares valley search program

LETAGROP [35J yielded the equilibrium constants f3i = 10-^ '^i ^nd ^2
166 ION-SELECTIVE ELECTRODES

1.00

0.90

0.80

0.70

1 1 1 +

+

^'''^LOPE CORRESPONDS

lU log P2"'^-'^ + +

0.783^

+ +

f

1 I 1 10 20 30

Figure 7. Expanded plot of Figure 6 in the region near x = 0, showing the intercept. Data

from Reference 27. = 104 03 in 3yv/ KCl medium, with no evidence for polynuclear or higher

mononuclear complexes. The results of a number of studies on this system by various methods are summarized in Table 3. The results obtained with a LaFs membrane electrode are in excellent agreement with

results obtained by other methods. Compare particularly the two most

recent studies in 3M KCl medium [26]. Three other fluoride equilibria have also been studied using the LaFs

membrane electrode. We have already mentioned the determination [24]

of /Csp for freshly precipitated LaFs by titration of La(N03)3 with NaF,

which gave a value K^^ = lO"^^ *^ at the ionic strength of the titration (~ 0.08M). Estimation of activity coefficients gave /Csp=10-^^^ at zero ionic strength. In the same study, the solubility product of EuFs was

determined to be 10"^^^-^ at ionic strength ~ 0. 1 , considerably larger

than for LaFs. The large discrepancy between the A^sp for freshly

precipitated LaFs and the effective A^sp for the solid LaFs crystal of the

electrode (~ 10^-^) has not yet been resolved.

The equilibrium constant for the reaction

+ F- ^ FeF+3 (21)
THERMODYNAMIC STUDIES 167

Table 3. Equilibrium constants for the — F- system at 25 °C. a

Method Ionic medium logKi log K2 Ref.

Conductance HF (var) 3.14 0.74 36

Cond. & Transference HF (var) 3.13 0.67 37

Solubility dilute 3.78 38

Colorimetric pH 0 3.62 1.52 39

Quinhydrone pH 0.53 KNO3 2.94 0.57 40

Quinhydrone pH 0.53 NH4NO3 2.82 0.59 40

Quinhydrone pH 0.53 NaNOs 2.91 0.57 41

T T 1 T T Hydrogen pH 0 (corr) 3.17 0.59 42

0.5 2.93 U.oU 42

U. lUz rldU4 3.15 0.59 42

Spectrophotometric pH u. 0 IN ai^lU4 2.91 A 0 43

Hydrocpn nH 3 KCl o.zo AA Quinhydrone pH 3 NaC104 3.28 1.08 44

LaF3 Membrane 1.0 NaN03 z.yu ± no 0.77 ± .05 27

LaF3 Membrane 1.0 NaN03 2.89 ± .01 0.86 ± .04 27

LaFs Membrane l.ONaCl 3.11 ± .03 90zz LaFa Membrane 3 KCl 3.31 ± .02 0.72 ± .03 26

Quinhydrone pH 3 KCl 3.32 ± .01 0.75 ± .06 26

Errors are 95% confidence limits where quoted.

Recalculated.
168 ION-SELECTIVE ELECTRODES

I \ \ \ I 0 0.01 0.02 0.03 Ch

Figure 8. Comparison of experimental with calculated values for fluoride concentration

in HF solutions of varying acidity. Data from Reference 26. was determined in the course of a kinetic study of complex formation

between fluoride and Fe+^ or Al+3 [29]. The method of analysis was

similar to that described for the HF complexes, except that hydrolysis of

Fe+3 had to be taken into account. The theoretical equation was obeyed

within experimental error, giving Ki = 10^-^^, and K2 < 10^, since the in- tercept was zero within experimental error. A study of the stability constants of Sn(II)-fluoride complexes has

been carried out using the lanthanum fluoride electrode [73], and some

more fragmentary studies deserve mention. Lingane [18] attempted

to determine the solubility product of CaF2 but this was not too successful. A similar attempt by Neumann and Sillen [26] also met with

difficulty due to unexplained drifts in potential. Lingane's solubility

product for CaF2 was 10-^ 27 which is much larger than the theoretical
THERMODYNAMIC STUDIES 169

value calculated from free energy data by Latimer [4] (10-^-^0 or from

conductance data by Kohlrausch [45] (lO-^o-^^). Clearly, more work is required on this system.

Some data have been published on the thorium fluoride complexes

[18], and some work is in progress on niobium fluoride complexes [26].

Complexes with Be+2, Zr^^, Al+3, and other ions have been noted

[20, 22, 29] but detailed studies have not been carried out. For example,

in 10-W BeS04 with IQ-W NaF at pH = 5.3, the potential of the

fluoride electrode is 125mV more positive than in 10"^M NaF alone

[20].

Fluoroborate ion apparently hydrolyzes enough even at room temperature to produce sufficient fluoride ion for the electrode to respond, but the

kinetics of hydrolysis are slow. For example [20], a solution of 2.5 X

IQ-'^M NaBF4 (which should produce IQ-^M fluoride on complete

hydrolysis) showed a potential 137.4mV more positive than a solution

containing only IQ-^M NaF. After 24 hours, this difference had decreased to 110.8 mV, and after 73 hours, to 85.1 mV. This experiment

suggests that the slow hydrolysis of BF4 would be simple to study

kinetically using the fluoride electrode, but that studies of the hydrolysis

equilibria would have to involve equilibration (if not measurement) at a higher temperature.

In contrast, fluosilicate ion showed essentially complete hydrolysis,

giving the same potential as a NaF solution containing the same amount

of total fluoride [20].

Deviations on the addition of more weakly complexed ions have also

been observed. This is shown in Figure 9 where the potential of the

lanthanum fluoride electrode {vs. SCE) in lO'^'M NaF together with additions of NaCl or MgS04 is plotted, as a function of ionic strength [17,20].

The broken line is the potential predicted by assuming the activity coeffi- cient of the fluoride ion to be equal to the mean activity of NaF at the same ionic strength, and neglecting any changes in liquid junction potential at the reference electrode. The calculated potentials agree with the

measured potentials in NaCl, NaNOa and Na2S04 solutions within

2 mV up to ionic strength 0.1 and within 7 mV at ionic strength 1.0. Although the measured potentials are all slightly positive of the calculated

potentials, and might be construed as showing some formation of NaF

complexes or ion-pairs, the deviations are not outside the range expected

from the approximations employed. On the other hand, the measurements

in MgS04 and MgS04-NaCl solutions show deviations in the same

direction of as much as 30 mV, which is a strong indication that fluoride

ion is being removed from the solution by formation of complexes,

probably MgF+. The existence of this complex has been suggested by

othe»- studies [3], but the present data are too sparse for evaluation of an
170 ION-SELECTIVE ELECTRODES

lO'"* !0"^ 10"^ 10'' I APPROX. IONIC STRENGTH

Figure 9. Potential of LaFs membrane electrode in 10~W NaF solutions containing vari- ous added electrolytes. equilibrium constant. However, this is certainly one system which could

be studied profitably using a constant ionic medium. One important point

to note is that an anionic interference by either Ch or SOj. would cause

the measured potential to be more negative than the predicted potential;

and the observed deviations are all in the opposite direction. A further

point to note is that the points on Figure 9 obtained by Frant and Ross

[17] in NaNO:5 and NaCl mixtures show experimental values close to those of Bock and Strecker [20] in NaCl alone. However, the values ob-
THERMODYNAMIC STUDIES 171

tained in Na2S04 [17] are almost precisely the predicted values, so that the large deviations observed in MgS04 must be due to the Mg++ ion and

not to the sulfate ion.

Although the stability and high selectivity of the lanthanum fluoride

electrode makes it eminently suitable for accurate measurements of activity coefficients, no results have yet been published in this area. However, there are at least two studies in progress, and these will be briefly

described here. The most obvious experiment to perform is the measurement of mean

activity coefficients in solutions containing only NaF by means of the

Na glass electrode |Na+, F", H2O | LaFs membrane electrode

and preliminary experiments of this type have been carried out [31,46].

The potentials obtained were consistent with the activity coefficients of

NaF in water, as obtained by isopiestic measurements [2], bu* the

reproducibility of the measurements (± 1 mV) was not as good as ex- pected. At the time, it was not clear whether this irreproducibility resulted

from instability in the sodium-sensitive glass electrode or in the LaFs

electrode, but subsequent experiments have provided evidence (including

visible etching of the glass surface) that the glass electrode is responsible

for the poor reproducibility of these measurements.

In our laboratory [31], we have also carried out measurements on NaCl-NaF mixtures using the following cells: Ag; AgCl I Na+, Ch, F-, H2O | LaFs membrane electrode

Ag; AgCl I Na+, Ch, F-, H2O | Na glass electrode

Measurements made with the first cell were much more reproducible than

those made with the second cell, and after some time, the sodium glass

electrode gave erratic response, required times as long as 1 hour to come

to equilibrium, and showed visible signs of etching on the surface. In contrast, the LaFs membrane electrode cell came to equilibrium within a few

seconds and showed no long-term signs of instability.

It is possible to obtain, from measurements of the AgCl-LaFs cell, the mean activity coefficients of both NaF and NaCl in NaCl-NaF mixtures.

The potential of this cell is given by

F. Activity Coefficient Measurements

cell:

(22)

348-381 0-69— 13
172 ION-SELECTIVE ELECTRODES

where mc\ and are the molal concentrations of chloride and fluoride in the mixed electrolyte, 712 is the mean activity coefficient of NaCl (component 1), and 721 is the mean activity coefficient of NaF (component 2)

in the mixed electrolyte. To eliminate long-term uncertainties in E°, the

test solutions are compared with a calibration solution with mci = mf. In order that Harned's Rule be applied, all solutions are the same ionic

strength (e.g., 1 .Omj. Since the concentrations of chloride and fluoride are known in both the test and reference solutions, and the temperature is known, the difference in potential between these solutions gives directly

the quantity

fi. = logf5^ (23)

Figure 10. Activity coefficient function /?2i (defined in text) as a function of X2, the ionic strength fraction of NaF in NaCl-NaF mixtures at constant total ionic strength \.0m. Data from Reference 3 1

.
THERMODYNAMIC STUDIES 173

If Harned's Rule is assumed to be obeyed for both components [ 1 ,2]

log 7i2 = log 7io — 0LX2X2I (24)

log 721 = log 720 — a2\XJ (25)

will hold, where 710 and 720 are the activity coefficients of NaCl and NaF,

respectively, in solutions containing only that salt, at ionic strength / which is the same as the mixed solution. The ionic strength fraction of

NaF, X2, is given simply by

X,= i-x,= (26)

Using these equations, one obtains

R2X = {oiri + OL2,){0.5 - X2) (27)

where we have made use of the fact that ^2 = 0.5 in the reference solution.Independently, from the Gibbs-Duhem relation, one obtains the rela- tion [1,2]:

«2i - «,2 = = 0.055 (28)

where 02 and are the osmotic coefficients of solutions containing

only NaF and NaCl, respectively, at ionic strength /. Combining this with

the above expression for /?2i, we obtain two alternative expressions:

R2X = (2 a,2 - 0.055) (0.5 - X2) (29)

R2X = (2 a2i + 0.055) (0.5 - X2) (30)

On Figure 10, a line has been drawn with the equation

R21 = 0.0034 - 0.0068 X2 (3 1

)

which leads to the Harned Rule coefficients

av2 = + 0.03 1 ; a2i = - 0.024 (32)

This value of ai2 is in good agreement with the results of measurements

with the AgCl-sodium glass electrode (Fig. 11), provided the data obtained at high values of X2 are discarded. This again confirms the inter- ference of fluoride ion with the sodium glass electrode. Some rather sparse data (Fig. 12) on a sodium glass electrode-LaFs membrane elec- trode cell have been obtained, and these are in good agreement with the

value ^21== +0.031.
174 lON-SELLCTIVE ELECTRODES

T

1 1 \ 1 \ 1 —

r

lel I I I I I I I I I I 0 .1 .2 .3 4 .5 6 .7 8 9 10

X , Figure 11. Mean activity coefficent of NaCl in NaCI-NaF electrolytes measured with

a sodium-sensitive glass electrode and an Ag-AgCl reference electrode. Xi is the ionic strength fraction of NaCl at constant total ionic strength 1.0m. Data from reference 31. From Figure 10 it is apparent that the data are also fit quite well by R21 = 0, the result which is expected on the basis of the Debye-Hiickel theory

if the sizes of the fluoride and chloride ions are approximately equal. If this assumption is made, one obtains

«,2 = - 0:21 =-0.0275 (33)

which is also in reasonable agreement with the other experiment.

Because of the apparent irreproducibility of the sodium glass electrode

in fluoride-containing solutions, experiments are in progress [31] to determine the activity coefficients of NaF and NaCl in these mixed elec- trolytes using a sodium amalgam electrode. This will provide an independent check on the results presented above.

G. Kinetics

The logical extension of equilibrium measurements to kinetic studies of

reactions involving fluoride ion has been made for three reactions by
THERMODYNAMIC STUDIES 175

NqCI-NqF

1=1.0 No glass -LaFj Cell O Beckmon + Corning

1.0

Figure 12. Mean activity coefficient of NaF in NaCl-NaF electrolytes measured with a sodium-sensitive glass electrode and a LaF.j membrane electrode. Data from Reference 31. Srinivasan and Rechnitz. In the reaction of Fe+^ with F-, they showed

that both the reaction paths

-f F- FeF+2 (34)

Fe+=^-hHF FeF+2 + H+ (35)

are possible at 25 °C, and depending on the pH, either F" or HF is the

primary reactant [29].

For the reaction of aluminum ion with F", the mechanism proposed

[29] is Al+^+HF ^ A1F+2 + H+ (36)

A1(H20)^^ + F- ^ A10H+2 + HF

A10H+=^ + HF A1F^=^ + H20

(37)

(38)

At high acidities the first reaction is rate limiting, and at lower acidities the third reaction becomes rate limiting. A study of the reaction between
176 ION-SELECTIVE ELECTORDES

iron(III) fluoride complexes with iodide ion has also been made [47] in which it was shown that Fe^^ (but not the complex FeF+2) reacts with

iodide ion. These data are discussed in more detail in Chapter 9. H. NoN-Aqueous Solutions

Although the fluoride electrode has not been used for thermodynamic

studies in solvents other than water, a few scattered observations seem to indicate that such studies can be done with a precision comparable to that obtained in aqueous solutions. Lingane [24] verified the Nernst equation

for the lanthanum fluoride membrane electrode (with respect to an aque- ous SCE) in 60% aqueous ethanol at ionic strengths (NaNOs supporting

electrolyte) of 0.1 and 0.0 IM. The free fluoride ion concentration at which deviations were observed from the Nernst plots was close to that value (10-Wj observed in aqueous solutions, but the potentials were ap- proximately 100 mV more negative. This may be either a liquid junction

or asymmetry potential effect, and quite possibly both.

Titration curves for fluoride with La(N03)3 in 70% aqueous ethanol

[24] and of fluoride with Th(IV) solutions in 60% aqueous ethanol [18]

indicate that the fluorides of these two elements are much less soluble in aqueous ethanol than in water alone, but no quantitative analysis of these

data to determine equilibrium constants was attempted.

Lithium has been determined by potentiometric titration with fluoride

using the lanthanum fluoride membrane electrode as indicator, in a sol- vent containing approximately 95% ethanol and 5% water, and it is clear from the titration curves that LiF is considerably less soluble than NaF

in this medium [48]. Again, no attempt was made to calculate equilibrium constants from the titration curve. Some preliminary experiments [49] have been conducted using the

lanthanum fluoride electrode in an aprotic organic solvent, dimethyl sul- foxide (DMSO). There appeared to be no visible attack or softening of the

material (Calcon polyester) from which the electrode body was prepared

in this solvent, and it seemed feasible to attempt potentiometric measurements. An aqueous SCE was used as the reference electrode. Lithi- um fluoride is known to be relatively insoluble in DMSO [50], and a sharp break was observed in a potentiometric titration curve of

tetraethylammonium fluoride (Et4NF) with LiCl, as shown in Figure 13. The solubility product obtained from this curve was within an order of

magnitude of the value (4x10^^) measured by direct solubility, but

quantitative consistency was not observed. This is further shown in Figure 14, which is an attempt to construct a Nernstian calibration curve

using varying concentrations of Et4NF in DMSO, both with and without

a supporting electrolyte. Although the electrode gave the expected

calibration curve in aqueous solutions, the response in DMSO solutions
THERMODYNAMIC STUDIES 177

-800ix-i-^l '

\

• \^ \ ^

I I \ i \ I L_j I I I 0 0.2 0.4 0.6 0.8 1.0 VOLUME, ml

Figure 1 3. Titration of Et4NF with LiCi in DMSO; +, with O.IM Et^NClO-, supporting

electrolyte; x, without supporting electrolyte. Data from Reference 49. was not all what was expected, and indicates that some material is present

which is removing free fluoride ion from the dilute solutions.

Tetraethylammonium perchlorate supporting electrolyte tends to increase

these deviations. Whether these mysterious results are due to impurities, or to some intrinsic difficulties with the LaFa membrane electrode cannot

be resolved without further experiments.

III. The Silver Sulfide Membrane Electrode

The silver sulfide membrane electrode responds to either silver ion or

sulfide ion in aqueous solutions. Nernstian response to Ag+ has been observed down to 10-W in AgNOs solutions, and to calculated Ag+ concentrations as low as \0-^^M in solutions of silver complexes. For silver ion concentrations below lO-^M, plasUc vessels are used because of the

strong adsorption of Ag+ by pyrex glass [51 J. The principal advantage ot the silver sulfide membrane over a simple silver metal electrode for deter- mination of silver ions is its freedom from interference by complexing and

precipitating agents (such as thiosulfate and iodide) and by oxidizing or reducing agents.
178 ION-SELECTIVE ELECTRODES

E VS. SCE, mV

Figure 14. Response of LaF^ membrane electrode to fluoride ion in DMSO: O EuNF

in OAM Et4NC104 supporting electrolyte: • Et4NF without supporting electrolyte;

, Nernst slope of 60mV. Data from Reference 49.

.
THERMODYNAMIC STUDIES 179

There have been only two published studies of this electrode, but it seems possible to exploit it in studies of a large number of chemical

systems involving either silver or sulfide. Hseu and Rechnitz [52], using an SCE reference electrode with an intermediate 0AM NaNOs salt bridge

to avoid reaction of sulfide with mercury ions or silver with chloride ions,

verified the Nernstian response to Ag+ over the range from 10-^ to 10"W, and to sulfide ion from 10 - to lO W. In the sulfide ion measurements, corrections had to be made for the reaction of sulfide ion with

water

S= + H20 ^ HS +OH- (39)

which is a significant reaction even in relatively concentrated NaOH

solutions. This effect (although well known) was verified by a study of the

effect of ph at consiant sulfide concentration. From the difference

between potentials observed in Ag+ solutions and S= solutions, the solubility product of Ag2S was determined to be (1.48 ±0.1) x lO"-^' at zero

ionic strength and 25 °C, in good agreement with literature data obtained

with silver electrodes and by calculation from free energy data. The effect of a number of anions was found to be negligible: Ch, Br-,

I~, SCN", CrOf, NO3" and SOf did not affect the response to sul- fide ion. Hg++ is probably the only cationic interference. The formation

constant Ks3 of the complex SnS§ from SnS2(5) and S= was deter- mined and found to be (2.06±0.1)x 10-^ at ionic strength 0.1 and 25 °C,

in agreement with the results of solubility measurements.

The response time of the silver sulfide electrode seems to be of the

order of 1 to 10 seconds, and thus kinetic studies of slow reactions involving sulfide ions seem to be feasible, although none have yet been

published [52]. On the other hand, if the electrode is first equilibrated

with the solution, it takes only a few milliseconds to establish the

equilibrium potential once the circuit is closed [53].

The response of the Ag2S membrane to silver and sulfide ions has been

verified by Light and Swartz [53], who also studied the temperature coefficient of the electrode. When the change in standard potential of the

Ag-Ag+ internal electrode is taken into account, the theoretical temperature coefficient in O.IM AgNOs solution was calculated to be idE/dT)th = —0.42 mV/deg, which is in good agreement with the experimental value

of -0.4 mV/deg. In0.1MNa2S and 0. IM NaOH, the temperature coeffi- cient is +0.05 mV/deg.

A comparison was made [53] between the silver sulfide membrane

electrode and a classical Ag-Ag2S electrode of the second kind, made by

coating a silver wire with silver sulfide. The membrane electrode was su- perior, parficularly with respect to interference by oxidizing agents such
180 ION-SELECTIVE ELECTRODES

as and nitric acid. The fundamental difference seems to be that the

electrode of the second kind has a porous structure which allows the solu- tion to come in contact with the silver electrode surface, whereas the

membrane electrode prevents this secondary path of reaction while

retaining the high ionic conductivity of the Ag2S crystal.

IV. Miscellaneous Solid-State Electrodes

Although thermodynamic studies have not been made with other

solid-state membrane electrodes, their ready availability may encourage

many studies in the near future. Membranes of the silver halides have some advantage over the conventional electrodes of the second kind,

since they are relatively unaffected by oxidizing agents, and can even be

made to show response to complexing agents such as SCN- and CN".

Electrodes reversible to divalent cations such as Cu++, Cd++, and Pb++

can also be prepared using mixed sulfides, and the construction and properties of these electrodes are discussed in Chapter 2. Heterogeneous

membrane electrodes may also be useful, but again, no serious ther- modynamic studies have been undertaken. Chapter 3 summarizes their preparation, properties, and history, so they will not be discussed further

in this section.

V. Calcium-Selective Electrodes

The calcium-selective liquid ion exchange electrode and a number of

related membrane electrodes have been the subject of considerable

research during the past three years. The calcium-selective properties of

a liquid ion exchanger based on calcium didecylphosphate dissolved in dioctylphenylphosphonate were first described by Ross [54], and other

membrane electrodes selective to calcium have been described by

Gregor, et al. [55,56], Shatkay [57,58] and Schultz et al. [59]. Much

earlier work is reviewed in these articles. Although the construction and

detailed properties of these electrodes (particularly interferences by

hydrogen, sodium, and other ions) vary, the general principles involved in evaluating them are similar to those we used in our discussion of the

lanthanum fluoride membrane electrode, and we will not belabor those

points here. Furthermore, calcium selective electrodes have been

discussed in great detail in Chapters 2 and 7, so this section will merely in- dicate those studies which are concerned with thermodynamic properties. In the case of the liquid ion exchange electrodes, the ion exchange

phase, a water-insoluble organic liquid, is immobilized in a porous membrane which separates two aqueous phases. A cell without liquid junction.
THERMODYNAMIC STUDIES 181

which we have used in our laboratory [60] may be represented as fol- lows:

Ag; AgCl(5) I CaCl2(mi) |organic | CaClsCma) | AgCl(5); Ag

(test) phase (internal)

and of course the organic phase may be a solid [59] as well as a liquid,

provided the cell resistance is low enough to permit accurate measurements. Measurements obtained with a concentration cell such as the one

described above are presented in Figure 15. Because there is no liquid

-100

CaCl2 — isopiestic data

X 0.1 m (98-20-02 exchanger)

+ O.lm ^

O 0.3 27m

A 0.843m ^ 1.02m

2.90nr ^

_l

(92- 20exchanger)

16

Figure 15.

•1.2 -.8 0 4

log(m y+)

1.2 1.6

Response of calcium-selective liquid ion exchange electrodes in CaCI.. solu- tions of various concentrations. The different sets of data were obtained with

different concentrations of internal filling solutions, as indicated. Data from

References 3 I and 60.
182 ION-SELECTIVE ELECTRODES

junction between the test phase and the reference electrode, there can be no ambiguity about the distinction between the liquid junction potential

and a single ion activity coefficient, such as is found in Shatkay's [56] ex- periments. A number of internal filling solutions were used (mz). and

when isopiestic values of the mean activity coefficient for CaCl2(7±) were

used, the Nernst equation

. ^ 3RT ^ TJiiyi \E = ^ln—^ (40) was verified within experimental error over a wide range of concentration. With the calcium didecylphosphate ion exchanger (Orion 92-20)

deviations from the Nernst equation were observed whenever the concentration gradient across the membrane was too large — either a test solution too concentrated for a dilute filling solution or a test solution too

dilute for a concentrated filling solution. Such deviations were observed

by Ross [54] with an 0.1m filling solution at concentrations above 0.1m

for test solutions, and were verified in later work [60] . However, if the in- ternal and external solutions are not too different in concentration, the

Nernst equation is obeyed over a limited range of concentration even in solutions as concentrated as 6m. A more recently available liquid ion

exchanger (Orion 98-20-02 exchanger, used in the "flow-through" ap- paratus) showed a much wider range of Nernstian behavior, even when

the internal solution was 0. Im and the external solution was 5m.

Data such as are presented in Figure 15 can also be used to determine

activity coefficients directly. In Figure 16 such a set of calculations is summarized. Using measurements on the most dilute solutions (<

0.0 1 m) with a dilute filling solution (0. 1 mj, it is possible to determine the

activity coefficient yi by extrapolation to infinite dilution. These data

show some deviations at high concentrations, but can be matched with activity coefficient data obtained with a more concentrated filling solution over the range where both systems show Nernstian behavior. Proceeding

in this way, one can build up piecemeal a curve of mean activity coeffi- cient from a number of different measurements, and such a curve is shown in Figure 16. The solid line represents the isopiestic data for the mean activity coefficient of CslCU [2]. In the above experiments, the pH of the test reference solutions was

kept at 7.0 to avoid interference by hydrogen ion, and also to avoid the

possible precipitation of Ca(OH)2 or CaCOa (due to atmospheric CO2).

These pH-dependent effects are discussed in Chapters 2 and 7, and must

be considered in any thermodynamic studies using calcium-selective elec- trodes. The stability of potential is not as good as with solid-state membrane

electrodes because the free charge at the organic-aqueous interfaces de-
THERMODYNAMIC STUDIES 83

1 T I CaClg

1

1 1 1 M

1 1 1

1 1 1 1

1

1 1 1 1/ 1-

-

isopiestic data

X 0 lm(98-20-02 exchanger)

O.lm A

O 0327m A 0.843m ^92-20 exchanger) V 102m

- 2 90m J X

- / -

lOmV -

1 / ~ / / /

/ V

o

X

1 , , , , 1 , .r— 1,1.

Figure 16. Results of analyzing the data presented in Figure 15 to obtain mean activity coefficients for CaCL. pends on the geometry of those interfaces, and even when the organic

phase is immobilized in a membrane, hydrostatic pressure, stirring, or sur- face-active agents can disturb the charge distribution which gives rise to the observed potential. Although readings can be duplicated to 0.1 mV.

overall errors are usually much larger. Thus, a system with carefully

reproducible geometry is essential for accurate studies. The response

time of the calcium-selective liquid ion exchange electrodes is of the order

of 10 seconds [61], considerably slower than for the solid-state membrane electrodes, but still fast enough for studies of the kinetics of slow

reactions.

Most divalent and monovalent cations interfere with the response of

calcium-selective electrodes to some extent, but the description of these

interferences is a complicated matter. In dilute solutions, the usual selectivity ratio concept is useful, and selectivity ratios are relatively constant over the range from 0.00 IM to 0.05M. Above this concentration, however, complicated ion-exchange equilibria, which have not been

thoroughly investigated, take place, and the selectivity ratio varies quite

strongly with solution composition. For example, the selectivity ratio of

the Orion 92-20 exchanger for calcium over sodium is approximately

5000 in dilute solutions [62], but this same exchanger in NaCl-CaCk

solutions of ionic strength 6m showed only about a 3-to- 1 selectivity ratio,

and this varied strongly with solution composition [60]. Selectivity ratios
184 ION-SELECTIVE ELECTRODES

-1 1 r

"1 r

Isopiestic Data

ao, = -O.OI65

experimental (98-20-02 ion exchanger)

NaCI-CaCI,

1= 3.15m

.151 1 1 1 1 1 I I I I I 0 I .2 .3 4 .5 .6 .7 .8 .9 1.0 (NaCI) Xg (CaClg) Figure 17. Results of an attempt to measure the activity coefficient of CaCU in NaClCaCl2 electrolytes using a liquid ion exchange electrode. Deviations from the isopiestic data [63] are in the direction expected if the electrode responded partially to sodium

ion. Data from Reference 3 1

.

for dilute solutions are given in Chapter 2, but these should be checked in

detail for concentrated solutions.

The Orion 98-20-02 exchanger, which showed better performance than

the 92-20 exchanger in concentrated CaCb solutions, was used in an at- tempt to measure the activity coefficients of CaCb in NaCl-CaCb elec- trolyte mixtures [31]. The results are shown in Figure 17. The straight

line at the top of the figure is obtained from the isopiestic data of Robin- son and Bower [63], which have been confirmed by measurements with

sodium glass electrodes and sodium amalgam electrodes [64]. The ex- perimental measurements obtained with the calcium-selective electrode

are in error by an amount well outside the random deviations of individual

measurements, and in the direction predicted if the electrode responded

to Na+ as well as to Ca++. These deviations are of the order of a few millivolts, and although this electrode system is not satisfactory for activity

coefficient measurements, it is still quite useful for analytical purposes.
THERMODYNAMIC STUDIES 185

Calcium-selective electrodes have also been used to measure equilibrium constants in a number of systems. Nakayama and Rasnick [65] measured the solubility product of calcium sulfate dihydrate and the dissociation constant of the complex CaS04 in aqueous solutions of varying ionic

strength containing NaCl and Na2S04. Their results were in good agree- ment with literature data obtained by solubility and conductimetric

methods [3].

Rechnitz and Lin [61] evaluated the equilibrium constants for the as- sociation of Ca++ with the chelating agents ethylenediaminetetraacetic

acid (EDTA) and nitrilotriacetic acid (NTA) using the Orion 92-20 liquid

ion exchanger. They also made a kinetic study of the exchange between

Ca++ and Mg++ with their EDTA complexes, which is described in more

detail in Chapter 9. Rechnitz and Hseu [66], using the Beckman 39068

calcium ion exchanger (which has a solid organic matrix [59]), studied

the formation constants of various complexes: calcium malate, calcium

citrate, and calcium rra/7^-1 ,2-diamino-cyclohexane-N,N,N^N'-tetraacetic acid (DCTA). In these studies, the electrode used had an advantage over the Orion liquid ion exchanger type in that it was much less sensitive to hydrogen ion, and measurements could be made in much

more acidic media. However, its selectivity for calcium over sodium was

poorer. Thompson [67] has measured the concentration of free magnesium ion

in a solution approximating sea water, using the Orion 92-32 ("divalent

ion") liquid ion exchanger, and obtained results in agreem^^nt with the cal- culations of Garrels and Thompson on their chemical model of sea water

[68]. A similar measurement of the concentration of ionized calcium in sea water was reported by Thompson and Ross [69]

.

Although measurement of activity coefficients for calcium salts in most

multicomponent electrolytes probably cannot be made with sufficient ac- curacy to compete with other thermodynamic approaches to such

systems, calcium ion activity measurements in such systems can be made

with sufficient accuracy and precision that the determination of equilibrium constants and the evaluation of the relative amount of ionized calcium

(or other divalent ions) compared to the total concentration in complex

mixtures may provide useful data, and in some cases, may provide the

only data available on a given system. The development of new and more

selective ion exchangers will continue to expand the field of measure- ments for which the calcium-selective ion exchange electrodes can be

used. VI. Miscellaneous Liquid Ion Exchange Electrodes

Although there are almost an infinite number of possible studies which

could be carried out with the various liquid ion exchange electrodes
186 ION-SELECTIVE ELECTRODES

available and yet to be developed, not much work of a thermodynamic

character has yet been published. A few studies will be briefly mentioned

here. Rechnitz and Lin [70] used a cupric ion-sensitive exchanger (Orion

92-29) to measure the formation constants of copper(II) with the ligands

glycine, glutamic acid, tris(hydroxymethyl)aminomethane, and acetate. Hseu and Rechnitz [71] used a perchlorate-sensitive exchanger (Orion

92-81) to determine the solubility products of KCIO4,

[Co(NH,)«](C104)3, [Cu(C5H5N)4](C104)2, and [Fe(C,2HHN2)3](C104)2,

where the latter two ligands are pyridine and 1 ,10-phenanthroline, respectively. Potterton and Shults [72] evaluated the precision (approximately

±1 mV), working range, response time (10 sec) and memory effects of

the nitrate-selective ion exchange electrode (Orion 92-07). The Nernst

equation was verified in NaNO;? solutions over the range of concentration

from 10"^-^ to 10"', but no further thermodynamic measurements were

made.

VII. Conclusions

The ready availability of solid-state and liquid ion exchange electrodes

which are more or less specific for certain ions has expanded enormously

the scope of experimental thermodynamic measurements in aqueous solutions. The solid-state electrodes (particularly the LaF.? membrane elec- trode) are stable and precise enough, and free enough of interferences by

other ions, that activity coefficient and equilibrium constant measure- ments should be possible in systems of quite varied complexity. Studies

of the coordination chemistry of fluoride compounds in aqueous and

non-aqueous solutions should burgeon with the advent of a fluoride ion

sensing device. Studies of equilibria and activity coefficients of halides

and pseudo-halides in the presence of oxidizing and reducing agents may

now be possible using appropriate solid-state membrane electrodes.

Similar restrictions on the use of silver electrodes and amalgam electrodes

of cadmium, lead, copper, and other metal ions, may be removed by the use of mixed sulfide solid-state electrodes.

Similarly, the liquid ion exchange electrodes reversible to ions such as perchlorate, nitrate, and tetrafluoroborate, greatly expands the scope of

thermodynamic measurements on compounds containing these anions,

and on their solutions. Although the precision and selectivity of these

electrodes is not as good as for the solid-state electrodes, it may be possible to make significant contributions to activity coefficient data as well as

to equilibrium constant data. The calcium-selective membrane electrodes

have already made extraordinary contributions to our understanding of

calcium in physiological systems, and it seems likely that they will continue to be of service in this area. In addition, the similar ion exchangers
THERMODYNAMIC STUDIES 187

which respond to other divalent cations may be employed in equilibrium constant measurements on systems which would otherwise require quite

indirect approaches.

This brief summary is only a beginning. We can look forward to many

years of exciting innovations in electrochemical thermodynamics as a

result of the application of ion-selective electrodes.

VIII. Acknowledgments

The author thanks Mrs. Rima Huston for her continual assistance

throughout the preparation of this review. Professor Lars Gunnar Sillen, Dr. Roger G. Bates, and Dr. Martin S. Frant contributed to important

discussions. This work was supported in part by the U. S. Department of

the Interior, Office of Saline Water.

IX. References

Harned, H. S., and Owen, B. B.,The Physical Chemistry of Electrolytic Solutions, 3rd ed., Reinhold Publishing Corp., New York, New York, 1 958. Robinson, R. A., and Stokes, R. H., Electrolyte Solutions, 2nd ed., revised. Butter- worth and Cox, Ltd., London, 1965.

Sillen, L. G., and Martell, A. E., Stability Constants of Metal-ion Complexes, Spec.

Publ. No. 17, The Chemical Society, London, 1964. Latimer, W. M., Oxidation Potentials, 2nd ed.. Prentice Hall, Englewood Cliffs, NewJersey, 1952.

Ives, D. J. G., and Janz, G. J., Reference Electrodes, Academic Press, New York,

1961. Harned, H. S., and Robinson, R. A., Multicomponent Electrolyte Solutions, Vol. 2, Topic 15 of the International Encyclopedia of Physical Chemistry and Chemical

Physics, Pergamon Press, London, 1968.

Butler, J. N., Adv. Electrochem. an,d Electrochem. Eng. Vol. 7 (in press). Smyrl, W. H., and Tobias, C. W., Electrochim. Acta 13, 1581 (1968): SmyrI, W. H., and Newman, J.. J. Phys. Chem. 72,4660 (1968). Bjerrum, J., Metal Ammine Formation in Aqueous Solution, P. Haase and Son, Copenhagen, 1941. Buck, R. P., Anal. Chem. 40, 1432, 1439(1968).

Bates, R. G., Determination of pH, Theory and Practice, John Wiley and Sons, Inc.. New York, 1964. Eisenman, G., Ed., Glass Electrodes for Hydrogen and Other Cations, Marcel Dekker, Inc., NewYork, 1967. Truesdell, A. H., Science 161,884(1968).

Moore, E. W.,and Ross, J. W.,Jr.,J. Appl. Physiol. 20, 1332 (1965). Lanier, R. D.,J. Phys. Chem. 69, 3992 ( 1 965). Synnott, J. C, and Butler, J. N., J. Phys. Chem. 72, 2474 (1966).

Frant, M.,and Ross, J. W., Jr., Science 154, 1553 (1966). Lingane, J. J., Anal. Chem. 39, 88 I ( 1 967). Durst, R. A., and Taylor, J. K., Anal. Chem. 39, 1483 (1967). Bock, R., and Strecker, S., Z. Anal. Chem.235, 322 (1 968).
188 ION-SELECTIVE ELECTRODES

[21] Baumann, E. W., Anal. Chim. Acta 42, 127 (1968). [22] Mesmer, R. E., Anal. Chem. 40, 443 (1968). [23] Gatewood. J., Halliburton Services, Duncan, Oklahoma 73533, private communication. [24] LingancJ.J., Anal. Chem. 40, 935 (1968). [25] Durst, R. A., Anal. Chem. 40, 931 (1968). [26] Neumann, G., and Sill6n, L. G., Royal Institute ot Technology, Stockholm, Sweden,

private communication.

[27] Srinivasan, K.,andRechnitz,G. A.,Anal. Chem.40,509(1968).

[28] Zielen, A.J.,J.Phys. Chem. 67, 1474(1963).

[ 29] Srinivasan, K., and Rechnitz, G. A., Anal. Chem. 40, 1 8 1 8 ( 1 968). [30] Raby, B., and Sunderland, W. E., Anal. Chem. 40, 939 (1968). [31] Huston, R., and Butler, J. N., Tyco Laboratories, Inc.. unpublished data (This work

was supported by the U. S. Dept. of the Interior, Office of Saline Water).

[32] Rossotti, F. J. C, and Rossotti, H., The Determination of Stability Constants, Mc- Graw HilK New York, 1961 , Chapter 5. [33] Butler, J. N., Ionic Equilibrium, Addison-Wesley, Reading, Mass., 1964, Chapters 8 and 9. [34] Ciavatta, L., and Liberti, A., International Conference on Coordination Chemistry,

London, 1 959, pp. 133-4. [35] Sillen, L. G., Acta Chem. Scand. 16, 1 59 ( 1 962); 18, 1085 (1964); lngri,N.,and

Sillen L. G., Acta Chem. Scand. 16, 1 73 ( 1 962); Arkiv Kemi 23, 97 ( 1 964). [36] Ostwald, W., J. Prakt. Chem. 32, 300 (1885); Duessen, E., Z. Anorg. Chem. 44,300

(1905). [37] Davies, C. W., and Hudleston, L. J.. J. Chem. Soc. 125, 260 ( 1 924). [38] Aumeras, A.,Compt. Rend. 184,1650(1927).

[39] Roth,W. A., Annalen542,35 (1939). [40] Brosset,C.,SvenskKem.Tidskr. 54, 155 (1942). [41] Brosset,C.,andWahlberg, U.,Svensk Kem. Tidskr. 55, 335 ( 1943). [42] Broene, H. H.,and DeVries, T., J. Amer. Chem. Soc. 69, 1644(1947).

[43] Connick, R. E., and Tsao, M. S., J. Amer. Chem. Soc. 76, 53 1 1 ( 1954), 78, 1827

(1956). [44] Ciavatta, L., Arkiv, Kemi 21, 129 (1963). [45] Kohlrausch, F.,Z. Rhys. Chem. 64, 129(1908).

[46] Bates, R. G., National Bureau of Standards, private communication.

[47] Srinivasan, K.,and Rechnitz, G. A., Anal. Chem. 40, 1955 (1968). [48] Baumann, E.W., Anal. Chem. 40, 1731 (1968). [49] Holleck, G., and Butler, J. N., Tyco Laboratories, Inc., unpublished data (This work

was supported by the U. S. Air Force, Cambridge Research Laboratories). [50] Butler, J. N., J. Electroanal. Chem. 14,89(1967).

[51] Ross, J. W., and Frant, M., paper presented at Eastern Analytical Symposium, New

York, Nov. 1968. See also Bulletin No. 3 and Instruction Manual for Model 94-16

electrode, Orion Research Corp., Cambridge, Mass., 1 967 and 1 968.

[52] Hseu,T. M.,and Rechnitz, G. A., Anal. Chem. 40, 1054(1968).

[53] Light, T. S., and Swartz, J. L., Anal. Lett. 1,825 (1968). [54] Ross, J. W., Science 156, 1378(1967).

[55] Gregor, H. P., and Schonhorn, H., J. Amer. Chem. Soc. 79, I507[1957]; ibid. 81, 391 1 (1959); ibid. 83, 3576 (1961). [56] Bagg,J., and Gregor, H. P., J. Amer. Chem. Soc. 86, 3626 ( 1 964). [57] Shatkay, A., Anal. Chem. 39, 1056 (1967). See also discussion Anal. Chem. 40,456

(1968). [58] Shatkay, A., J. Phys. Chem. 71, 3858 ( 1 967); Biophys. J. 8, 9 1 2 ( 1 968).
THERMODYNAMIC STUDIES 189

[59] Schultz, F. A., Peterson, A. J., Mask, C. A., and Buck, R. P.. Science 162, 267

(1968). [60] Huston, R., and Butler, J. N., Anal. Chem. 41, 200 (1969). [61] Rechnitz,G. A., and Lin,Z. F., Anal. Chem. 40, 696 ( 1 968). [62] Moore, E. W., Ann. N. Y. Acad. Sci. 148 ( 1 ) 93 ( 1 968). [63] Robinson. R. A., and Bower, V. E.,J. Res. Nat. Bur. Stand. 70A, 3 1 3( 1 966). [64] Butler, J. N., and Huston, R., J. Phys. Chem. 71, 4479 (1967). [65] Nakayama, F. S., and Rasnick, B. A., Anal. Chem. 39, 1022 (1967). [66] Rechnitz,G. A., and Hseu,T. M., Anal. Chem. 41, 1 1 1 (1969). [67] Thompson, M. E., Science 153, 866 ( 1 966). [68] Garrels, R. M., and Thompson, M. E., Amer. J. Sci. 260, 57 ( 1 962). [69] Thompson, M. E.,and Ross, J. W., Jr., Science 154, 1643 (1966). [70] Rechnitz,G. A., and Lin,Z. F., Anal. Lett. 1,23 (1967). [71] Hseu,T. M.,and Rechnitz, G.A., Anal. Lett. 1,629 (1968). [72] Potterton,S. S.,andShults,W. D.. Anal. Lett. 1, 1 1(1967).

[73] Hall, F. M., and Slater, S. J., Australian J. Chem. 21, 2663 (1968).

CHAPTER 6

ACTIVITY STANDARDS FOR

ION-SELECTIVE ELECTRODES

Roger G. Bates and Marinus Alfenaar^

Division of Analytical Chemistry

National Bureau of Standards

Washington, D.C. 20234

I. Introduction. Electrode Response and Ionic Activity

Measurement of the electromotive force of reversible galvanic cells is one of the most attractive means available for studying the properties of

the electrolytes participating in the cell reaction and, by extension, of the

ions of which they are composed. Difficulties are encountered, however,

in separating the emf, a potential difference, into its two electrode potentials. There is a corresponding difficulty in separating the well-defined

properties of an electrolyte into those for the individual ions; here ther- modynamics can offer no unique guide or formula.

Nevertheless, the concepts of the single electrode potential and the in- dividual ionic activity are useful. In this connection, it is interesting to note that the utility of a conventional scale of electrode potentials has

been recognized for many years, although many thermodynamic purists

continue to oppose the concept of single ion activities. In essence, the indeterminacy of electrode potentials and single ion activities stems from the indeterminate character of the surface potential of

any real phase and of the inner electric (Galvani) potential <I>, [1,2]. The

outer (Volta) potential ^ of the phase, a measurable quantity, is defined

by the work required to bring a unit point charge very slowly from an in- finite distance up to a point close to the surface of the phase. To obtain the

inner potential of the phase, however, it would be necessary to know the

surface potential or the work of moving the point charge through the

surface. These quantities are related by

o = ^+x (1)

The surface potential x is not measurable. For this reason, the Galvani

potential <I> within a single phase cannot be determined exactly, nor can

the difference of Galvani potentials between points in different phases (on

which the single electrode potential depends) be measured. On the other

hand, Galvani potential differences corresponding to the transfer of ions

' Present address: Analytical Chemistry Laboratory, University of Utrecht, Croesestraat 77A, Utrecht, Netherlands. 191
192 ION-SELECTIVE ELECTRODES

between internal parts of the same phase can be measured readily because

they do not involve the indeterminate surface potential.

The electrochemical process at an electrode always involves a transfer of charge from one phase to another. When two electrodes are immersed

in the same liquid phase, however, the surface potential cancels out. Consequently, the electric potential difference, under zero current conditions,

between two pieces of the same metal attached to the electrodes depends

solely on the chemical potentials of the substances participating in the

electrode reaction. This potential difference is termed the electromotive

force (emf).

Cell reactions are oxidation-reduction processes. It is convenient to think of two half reactions, one (an oxidation) supplying electrons which, on closing an external circuit, pass to the other electrode and are con- sumed in a reduction process. Consider a cell represented by the scheme

Zn(5) I Znl2(m) | Agl{s);Ag{s)

where (s) denotes a solid phase and (m) represents the molality of zinc

iodide in the solution phase. Clearly zinc and silver both exist in two oxidation states in the two electrode compartments. The half reactions are Zn2+ 4- 2e- ^ Zn (2)

and

Agl-^e- ^ Ag + I- (3)

These half reactions are reversible, and it is impossible to tell, without

further information, which will proceed toward the right (reduction) and

which toward the left (oxidation) when the zinc and silver electrodes are connected with an external conductor. Hence, by international convention [3], cell reactions are written as if oxidation occurs spontaneously at the left electrode of the cell scheme and reduction at the right on closing

the external connection. This situation would make the right electrode

positive to the left, and, when these conditions are met, the emf is given a

positive sign. If, in actuality, the left electrode is found to be the positive

electrode, the emf is given a negative sign [3]

.

The cell reaction for the cell given in the above example is therefore

Zn + 2 Agl ^ Znl2 + 2 Ag (4)

Thus, Equation (2) is assumed to proceed spontaneously from right to left (oxidation) while Equation (3) proceeds from left to right (reduction). According to the Nernst equation, the emf, E, of the cell is given by

E = E°- —\n (azn2+ a?-) (5)
ACTIVITY STANDARDS 193

where R, T, and F are respectively, the gas constant, the thermodynamic

temperature, and the faraday.

Furthermore, conceptually it may be said that the potential of the zinc

electrode is determined by the activity of zinc ions and that the potential

of the silver-silver iodide electrode is determined by the activity of iodide

ions, even though only the mean activity of these ions is measurable. Formally, the potentials of the two electrodes can therefore be written

[compare Eq. (2) and Eq. (3)] RT

£'zn2+; Zn=^Zn2+; Zn-^ 2f^ri azn2+

and

EAgl'^Ag — EaqJ -^Ag Y~

By convention, the emf of the complete cell is Er — Ei, where r and / denote the right electrode and left electrode, respectively.

II. Operational Definition of the pA Value

The convenience and practicality of routine pH measurements were as- sured by the development of the glass electrode. The potential difference

between this electrode and the solution in which it is immersed responds

rapidly and precisely to changes in the activity of hydrogen ions in the

solution. The pH cell consists of a glass indicator electrode combined

with a stable reference electrode of substantially constant potential.

The development of other ion-selective electrodes responding satisfactorily to ions other than hydrogen makes possible a similar solution of the

problems of measuring the concentrations or activities of these ions in solution. An ion-selective electrode A{sel) reversible to the cation A"+,

for example, can be made a part of the cell Aisel) I A"+ 1

1 KCl(conc) | Hg2Cl2;Hg

where the electrode on the right is a standard calomel reference electrode.

An electrode reversible to the anion A"- can be used similarly:

A(sel) I A"- II KCl(conc)| Hg2Cl2;Hg

The reactions for the two cells are: A +

I

Hg2Cl2 ^ A"+ + n Hg -H n C\- (in cone KCl) ± ion transfer (8) and

A"- + ^ HgzCls A + nUg + n CI- (in cone KCl) ± ion transfer (9)

(6)

(7)
194 ION-SELECTIVE ELECTRODES

Inasmuch as the chloride activity in the reference electrode is constant

(barring temperature changes), the term (RT/F) (In aci-) can conveniently be included in the standard potential of the reference electrode

(as is often done in discussions of pH cells [4]), the combination being

termed E°e'f. Hence, for the emf, E, of the cell with an electrode reversi- ble to a cation, one can write

{EVef+Ej) -El-^lnaj,n+ (10) nr where Ej is the liquid-junction potential, and, for the corresponding cell containing an electrode reversible to an anion,

E={E%f+Ej)-El^^\na^^n- (11)

It is evident that the emf of the first cell [compare Eq. (10)] decreases

with increasing activity of A"+, while that for the second [compare Eq.

(11)] increases as the activity of A"~ becomes greater.

The operational definition of pH [5 ] was a necessary consequence of

the inability to evaluate terms such as E°Jf4-Ej and of a recognition

of the day-to-day drifts in E\. For this reason, the pH is defined in terms

of the difference of emf between the "unknown" solution, X, and a stan- dard, S, of similar composition, the two measurements preferably being

made at nearly the same time. It is logical to extend this approach to the

measurement of "pA." From Equation (10), E°Jf, Ej, and E°x remaining unchanged, the difference of E observed when a standard solution is replaced by an unknown solution is a quantitative measure of the dif- ference of pA:

pA(X) = pA(S).iL(^=^^ 02)

when A is a cation. Similarly, from Equation 1 1 , for an anion A,

pA(X) = pA(S)-^^^|^^^^ (13)

III. The Residual Liquid-Junction Potential

Tentatively, Equations (12) and (13) may be regarded as definifions of

the pA value when the selected ion is a cation, A"+ [Eq. (12)] and an

anion. A"- [Eq. (13)]. However, the likelihood that the residual

liquid-junction potential in pA measurements may be larger than in pH

measurements must not be overlooked. This quantity, expressed in pA or pH units, will be designated Af'j. It arises from differences in the con-
ACTIVITY STANDARDS 195

centrations and mobilities of the ionic species in the standard (S) and

unknown (X) solutions.

Because of the buffer effect, wide changes of pH are not necessarily ac- companied by appreciable changes of ionic strength; they may be

achieved by the substitution of other buffer species of much the same

molality. On the contrary, it is often difficult to vary pA without producing a corresponding change in the total concentration of ions. For example, an "unknown" solution of sodium chloride with pCl about 1 will have

10 times the ionic strength of a standard NaCl solution of pCl(S) = 2. These differences, which must be regarded as the rule rather than the ex- ception, make it imperative to include AEj on the right side of Equations

(12) and (13) at this stage in the development of definitions of the pA

value. The magnitude of A^"; can be estimated by the classical formulas

for the liquid-junction potential or by comparing the "experimental"

pA(X) with the "true" -log given by the convention adopted. Thus,

Af, = pA(X)+logaA(X) (14)

It is to be expected that later work will show how large a separation of

pA(X) and pA(S) can be tolerated before "greater than negligible" liquid

junction errors are encountered.

IV. Performance Tests for Ion-Selective Electrodes

The electrode potential of a well-behaved reversible ion-selective elec- trode responds to changes in the activity of the selected ionic species in conformance with the Nernst equation. In view of the fact that the varia- tions in the liquid-junction potential may well be large enough to obscure

the proper behavior of the indicator electrode, it is very desirable that the

electrode response be examined in a cell without liquid junction, if possible. In many instances, this can be accomplished by comparing mean activity coefficients for electrolytes, determined by the use of the ion-selective electrode, with accepted values obtained with electrodes of proved

reliability or by other thermodynamic methods. For example, ion-selective electrodes reversible to metal ions can often be combined with the re- liable silver-silver chloride electrode in solutions of the metal chloride. If the activity coefficients obtained from the measured emf values agree

with the accepted literature values, it may safely be assumed that the elec- trode is responding satisfactorily over the concentration range covered by

the measurements. Electrodes reversible to anions may be combined in a

similar way with the hydrogen electrode or with a metal electrode known

to be dependable.

This procedure is useful not only for affirming the Nernst response of

the electrode but also for examining the selectivity. For the latter pur-
196 ION-SELECTIVE ELECTROOES

pose, the mean activity coefficients of a salt of the selected ion in mixtures

of electrolytes are needed.

V. Conventional Activity Scales

Although the potential of a single electrode is believed to reflect changes in the activity of a single ionic species, it is quite clear that a) only

potential differences between individual electrodes can be measured, and

b) activities of ion combinations alone can be exactly determined. If the

reference electrode potential and its associated liquid-junction potential

are hopefully assumed to remain constant, however, emf measurements

lead to changes of ionic activity. The usefulness of practical pH measure- ments depends on such a procedure and on a defined or conventional scale of hydrogen ion activity on w hich reference standards for the pH scale are based.

A. The pH Convention

In the NBS procedure, standard pH(S) values are assigned to selected

buffer solutions with the aid of emf measurements of cells without liquid

junction. The cells contain hydrogen electrodes and silver-silver chloride

electrodes: therefore, they yield values of the acidity function piauyci) for the buffer solution with added chloride and. by suitable extrapolation,

also for the chloride-free buffer solution. A non-thermodynamic step, the

estimation of yn-. is necessary to derive values of pan. which are, in turn, identified with pH(S) for the reference standards in the operational

pH definition. With international concurrence [6]. the following convenfion for yci- was adopted:

where A is the Debye-Hiickel slope constant and / is the ionic strength.

It was intended that this formula be used at ionic strengths of 0. 1 and

below.

At this point it should be emphasized that, in theory, the activity coeffi- cients of other ions become fixed when a scale of numerical values for the

activity coefficients of any one species is selected. If jcr in a solution

of sodium chloride is defined, for example, yxa+ becomes fixed through

the mean activity coefficient y= of sodium chloride obtainable by a

variety of thermodynamic methods. In a similar way. yca2+ and yK+ in solutions of calcium chloride and potassium chloride, respectively,

acquire numerical values when yc\- in these solutions is evaluated.

Mean activity coefficients can also be measured in mixtures of electrolytes. Furthermore, certain combinations and rafios of ionic activity
ACTIVITY STANDARDS 197

coefficients, such as yci-/7Ac- (where Ac~ is acetate ion) and (yci-

• yH2For)/7HP02- can be determined by experimental means. The number of arbitrary non-thermodynamic formulas or conventions

adopted in an effort to facilitate and improve the interpretation of analytical measurements made with ion-selective electrodes (hydrogen and glass

electrodes must be included in this class) should evidently be kept as small as possible. Otherwise a truly chaotic situation would result. It is therefore highly desirable that standard reference data for the activities of

the ions to which the newer ion-selective electrodes respond be made as consistent as possible with the convention already adopted in the assignment of standard pH values.

B. Comparison of Reasonable Conventions

The pH convention is usually applied to the estimation of yci- in buffer solutions containing relatively small amounts of an alkali chloride.

The chloride ion activity coefficients derived by Equation (15) are, however, nearly the same as the mean activity coefficients of sodium chloride

in its pure aqueous solutions, up to an ionic strength exceeding 0. 1 . Thus,

in practice, the pH convention is substantially equivalent to a convention

which is based on the equality of 7Na+ and 7ci~ in these solutions of

sodium chloride. Consequently it is completely analogous to the Maclnnes

convention [7] which asserts the equality of 7k+ and yci- in aqueous

solutions of potassium chloride. The Maclnnes convention has been

widely used in the estimation of single ionic activity coefficients. Garrels

[8] has proposed that it be adopted as a basis for establishing activity

standards for ion-selective electrodes.

Both the pH convention proposed by Bates and Guggenheim [6] and

the earlier Maclnnes convention offer a means of achieving a certain

amount of consistency among the activity coefficients of a number of sin- gle ionic species. In practice, they are not completely successful in ful- filling this desired objective. Nevertheless, they may be expected to have some advantages over approaches based solely on a splitting of the mean

activity coefficients of all electrolytes according to a predetermined for- mula. For uni-univalent electrolytes, the simplest convention of this type

is y+ = y- = y+. For 2-1 electrolytes such as calcium chloride, it is reasonable, as Butler has pointed out [9], to interrelate the activity coeffi- cients of the ions according to the valence relationships set forth in the

Debye-Huckel equation, namely 72+^7^=^7!. This convention, in turn, appears somewhat more reasonable than equating 72+ to y± as Shatkay has proposed for calcium chloride [10].

Table 1 compares the values of lpa^ for several cations and anions in aqueous salt solutions at ionic strengths of 0. 1 and 1 .0, as derived by three
198 ION-SELECTIVE ELECTRODES

of these conventions. It is evident that these "reasonable" conventions

give closely comparable results at ionic strengths of 0. 1 or less but that the differences become appreciable when the ionic strength is as high as

1.0. Table 1. Comparison of values of pa^ based on three different conventions.

Salt pH convention

PaA

Maclnnes

convention

Debye-Hiickel

convention

cation anion cation anion cation anion

Ionic strength = 0.1 KCl 1.118 1.114 1.114

1.110 1.114 1.114

NaF 1.108 1.106 1.116

1.124 1.126 1.116

NaCl 1.108 1.106 1.110 1.112 1.114 1.110

Nal 1.108 1.106 1.104

1.100 1.102 1.104

NaClO^ 1.108 1.106 1.111

1.114 1.116 1.111

CaCl2 1.887 1.880 1.898

1.286 1.291 1.282

Ionic strength = 1.0 KCl 0.234 0.219 0.219

0.204 0.219 0.219

NaF 0.160 0.145 0.242

0.324 0.339 0.242

NaCl 0.160 0.145 0.182

0.204 0.219 0.182

Nal 0.160 0.145 0.133

0.106 0.121 0.133

NaC104 0.160 0.145 0.201

0.242 0.257 0.201

CaCl2 1.105 1.075 1.168 0.381 0.396 0.349
ACTIVITY STANDARDS 199

C. Self-Consistent Scales of Ionic Activity

In the application of the pH convention a further problem — that of

internal consistency — arises. The same difficulty must be faced in ap- plying the Maclnnes convention. This dilemma is illustrated by the fol- lowing diagram:

Convention

>'NaCl >'NaBr >'NaNOc >^N0;

>'KC1 >^Br

>'CaCL yfca^- >^CaBr. >^Br >'Ca(N03)2'

The activity coefficient of chloride ion in solutions of varying ionic

strengths is defined by the convention embodied in Equation (15). With

a knowledge of mean activity coefficients, it is then possible to obtain

the activity coefficients of sodium, potassium, and calcium ion, for example, in solutions of their chlorides. If the activity coefficients of

these cations were taken, by extension, to be the same in bromide or

nitrate solutions, for example, three or more pathways to ygr- and

7no3 would be available. Without doubt, these multiple values of ygr- and y^o^ would differ from one another at higher ionic strengths. One

value, of course represents yer in a sodium bromide solution, another

in a potassium bromide solution, and so forth. It is quite reasonable that these should be different, but it must not be forgotten that the separate

values of y^^- were derived by taking 'yNa+ (or 7k + ) to have the same value

in the chloride and bromide salt solutions of the same ionic strength.

According to this approach, multiple pathways to the activity coeffi- cients of single ions exist. For example, yp,- could be calculated by a
200 ION-SELECTIVE ELECTRODES

number of independent paths from the convention for yci- and the mean

activity coefficients of MA and MCI, where M represents any one of a number of univalent cations:

log 7a- = log 7ci- + 2 log ( 1 6)

Similarly, 7a- could be derived from data for the salts of bivalent

cations M^+i

log 7a- = log 7ci- +1 log^ (17) ^ 7mci2 The individual values obtained at ionic strengths of 0. 1 and 1 .0 are sum

marized in Table 2. It is clear that the choice of pathway is not very sig- nificant at an ionic strength of 0. 1 . Again it is evident that larger inconsistencies are encountered at higher ionic strengths, where the mean activity coefficients of salts of the same valence type become increasingly

divergent.

We are not inclined, at the present stage in the development of

ion-selective electrodes, to propose pathways leading to single-valued

ionic activities for all ions in all of their salt solutions. We prefer rather to deal first of all with the restricted number of standard solutions required

for the calibration of the electrodes in most common use and to elaborate

other pathways when the need for them is demonstrated.

It is therefore proposed that, to the fullest extent possible,

cation-responsive electrodes be standardized in solutions of the cor- responding completely dissociated chloride salts and that anion-responsive electrodes be standardized in solutions of the completely dissociated

sodium salts of the anions. Activity coefficients for the "reference" ions

chloride and sodium would be derived from the pH convention directly

and from its combination with the known mean activity coefficients of

sodium chloride in its aqueous solutions:

log 7Na+ = 2 log 7:t (NaCl) - log 7c,- (18)

It is further suggested that these rules apply without restriction as to ionic

strength.
ACTIVITY STANDARDS 201

Table 2. Values of -log for anions at 25 °C, derived from the pH

convention by different pathways.

Cation Anion (A)

cr F" Br~ T

1 cio- NO3-

Ionic strength ^- 0.1

Li+ 0.110 - 0.10 0.08 0.09 0.11

Na^ 0.110 0.12 0.11 0.10 0.12 0.13

0.110 0.10 0.11 0.10 - 0.14

Rb+ 0.110 0.11 rv -1 -I 0. 11 - 0.14

Cs+ 0.110 0.11 0.11 0.14

0.110 0.10 0.09 0.09 0.11

Ca2+ 0.110 0.11 0.10 0.10 0.14

Sr2^ 0.110 0.11 0.10 0.11 0.14

Ba2+ 0.110 0.09 0.08 0.09 0.13

Ionic strength = i.U Li+ 0.204 0.17 0.06 0.09 0.24

Na+ 0.204 0.32 0.16 0.11 0.24 0.36

0.204 0.15 0.19 0.15 - 0.47

Rb+ 0.204 0.21 0.22 _ 0.47

Cs+ 0.204 0.21 0.22 0.42

Mg2- 0.204 0.15 0.09 0.07 0.22

Ca2^ 0.204 0.16 0.10 0.09 0.30

Sr2+ 0.204 0.17 0.10 0.14 0.33

Ba2+ 0.204 0.16 0.09 0. 14 0.46

VI. Standard Reference Solutions

Standard reference values for p«ci and p«Na in sodium chloride solu- tions and for p^ca in calcium chloride solutions and p^p in sodium fluoride

solutions have been based on the procedures set forth in the preceding

section. The results are given in Table 3 for several molalities of the
202 ION-SELECTIVE ELECTRODES

reference salt solution. By definition, the conventional pax in these

selected standard reference solutions will be identified with pA(S) in the

operational definitions set forth in Equations (12) and (13). The mean activity coefficients needed in the calculation of paa were taken from data

in the literature (NaCl [11.12]:NaF [13]: CaCl. [14,15]). In view of the

likelihood that sodium fluoride is not completely dissociated in the range

of molality 0. 1 to 1 .0, it was not possible to assign a standard value for pF

in \m sodium fluoride. VII. Comparison of Experimental and Defined pA Values

We have examined the behavior of chloride electrodes as well as those

responsive to sodium, calcium, and fluoride ions in relation to the scales of ionic activity proposed in the previous sections. In each case, the

response of the electrode was determined in a cell without liquid junction,

in combination with a "norm" electrode known to behave reliably in the

solution in question. After the response of the electrode had been af- firmed in this way, pA values were obtained experimentally over a wide

range of electrolyte concentration. The "experimentar" values of — log y^,

that is, pA + log fn^, were compared with — log defined by the conventions set forth above. For the measurements, the electrode was stan- dardized at an ionic strength of 0.01 . The pA values at this reference point can be found in Table 3. Table 3. Suggested reference standard values, pA(S). at 25 °C.

Material Molality pNa(S) pCa(S) pCKS) pF(S)

mol kg".-1 NaCl 0.001

0.01

0.1

1.0

3.015

2.044

1. 108

0.160

3.015

2.044

1.110

0.204

NaF 0.001

0.01

0.1

3.015

2.044

1.108

3.015

2.048

1.124

CaCl2 0.000333

0.00333

0.0333

0.333

3.537

2.653

1.887 1.105

3.191

2.220

1.286

0.381
ACTIVITY STANDARDS 203

The emf measurements of cells without liquid junction were made in U-type cells, the two compartments of which were joined by capillary

tubing. Another cell vessel accommodated two ion-selective electrodes

in a main chamber provided with a magnetic stirrer. Two side compartments, separated from the main chamber by stopcocks, housed the

calomel reference electrodes. This vessel was immersed in a water bath

for temperature control. The measurements in sodium fluoride solutions were made in beakers and other laboratory ware fabricated of

polyethylene. Three commercial saturated calomel reference electrodes were used in this work. Twojunctions were of the fiber type, and the third was of the sleeve type. The measuring equipment consisted of a precision

potentiometer, a high-impedance electrometer of the vibrating reed type,

and a recorder.

It should be emphasized that the observations on electrode behavior

recorded in the succeeding sections were made on a single electrode

of each type studied. Individual variations among electrodes of the same type certainly exist. Furthermore, improved types of ion-selective

electrodes are being developed continually by a rapidly advancing

technology.

A. Chloride-Selective Electrodes

Two commercial types of chloride-selective electrodes (Orion

Research, Inc.), namely the solid-state type (Model 94-17), consisting of

a silver chloride membrane, and the liquid ion-exchanger type (Model

92-17) were used. These were compared in sodium chloride solutions

directly against a silver-silver chloride electrode, with the results shown

in Figure 1 . The response of the solid-state electrode was found to be su- perior to that of the liquid ion-exchanger electrode. The measurements

were usually made in stirred solutions, and equilibrium was ordinarily at- tained in less than 15 minutes, provided that the silver-silver chloride

electrode had been suitable conditioned. The results obtained below a

molality of 5 X 10^^^ mol kg'\ where the silver-silver chloride electrode

is poorly reproducible, are not to be considered significant. In repeated measurements of cells containing a chloride-selective

electrode and a silver-silver chloride electrode in 0.01 m sodium chloride,

the solid-state electrode was found to require 15 min to achieve equilibrium at 10 °C. Shorter response times, of the order of 3 to 7 min, were observed at 25 and 45 °C. Reproducibility was about 0.01 pCl unit. In sodium chloride solutions, the reproducibility and response time of the

liquid ion-exchanger electrode were slightly superior to those of the

solid-state electrode at all three temperatures. Prior to each measurement,

the ion-selective electrodes were soaked in distilled water and dried with

absorbent tissue.
204 ION-SELECTIVE ELECTRODES

cell: CI (sel)|NaCI (m)|AgCI ; Ag

-5 -4 -3 -2 -I 0

Figure L Comparison of two types of chloride-selective electrodes with the silver-silver chloride electrode in solutions of sodium chloride.

When pA values were measured with the chloride-selective electrode

(solid-state type) standardized at / = 0.01 in sodium chloride solutions,

the results shown in Figure 2 were obtained. The curves represent

theoretical values of — logyci- calculated by the pH convention set forth

in Equation (15) [curve 1], by the Maclnnes convention as proposed by

Garrels [curve 2], and setting yci- equal to the mean activity coefficient

of sodium chloride in these solutions [curve 3j. Inasmuch as the response

of the solid-state chloride-selective electrode was shown to follow closely

that of the silver-silver chloride electrode from 5x lO^-'m up to 1.0m,

the departure of the experimental points from the curves of Figure 2 must be due either to residual liquid-junction potentials or to inadequacies

in the three conventions.
ACTIVITY STANDARDS 205

0.4

6mV 2 0

CDO

'_ 0.2

o

0 t NaCI

-0.2

-3 -2 -I 0

log I

Figure 2. "Experimental" values (circles) of -log ycr. derived from emf measurements

with a chloride-selective electrode and a calomel reference electrode, compared with

values defined by three conventions. Curve 1, pH convention; curve 2, Maclnnes convention; curve 3, ycr = 7±(NaCl). Arrows mark point of standardization.

A sodium glass electrode of composition NASn-is (obtained from

Corning Glass Works, Inc.) was combined with the silver-silver chloride

electrode in sodium chloride solutions; the cell had no liquid junction:

The standard potential was calculated from the emf at m = 0.01 and the

activity coefficient for sodium chloride at this molality [12]. Results of

the emf measurements are shown in Figure 3. The mean activity coeffi- cients of sodium chloride calculated from the measured emf are shown by

the circles, and the curve is drawn through the accepted activity coeffi- cients given in the literature [12,13]. The accuracy of the response of the

sodium electrode seems to have been confirmed in the range of sodium

chloride molalities from 0.001 to 1.0 mol kg-^

At 25 and 45 °C, the sodium glass electrode reached equilibrium in about 3 min. Its behavior at 10 °C was inclined to be sluggish, probably

because of the increased electrical resistance of the glass membrane when

B. Sodium-Selective Electrode

Na(^^/) I NaCl(m) | AgCl;Ag
206 ION-SELECTIVE ELECTRODES

0.2 - CELL:Na(gl)|NaCl(m)|AgCI; Ag

0.1 o

o

O

-0.1 -3 -2 -I 0

Figure 3. Determination of -log 7^301 with the sodium glass electrode in a cell without

liquid junction. The curve is drawn through the accepted literature values. the temperature was lowered. At the two higher temperatures, the

reproducibility of repeated measurements was very good, being of the

order of 0.1 to 0.2 mV(0.002 to 0.003 pNa unit).

The response of the sodium glass electrode in mixtures of sodium

chloride and calcium chloride at a constant ionic strength of 1.0 was also confirmed by emf measurements of the cell

at 25 °C. The values of log (yNaci/yNaci) ^ where yNaci is the activity

coefficient of sodium chloride in its pure aqueous solution of molality

1.0 mol kg"^ agreed within 0.001 unit of those calculated by Robinson

and Bower [16] from isopiestic vapor pressure measurements.

The "experimental" values of pNa were obtained by means of a cell with liquid junction, consisting of the sodium glass electrode in combination with a saturated calomel reference electrode, the cell being stan- dardized as before in a sodium chloride solution of molality 0.01 mol kg~^

The results are shown in Figure 4. As in Figure 2, curve 1 was derived

from the convention proposed here, curve 2 represents the Maclnnes

convention, and curve 3 is based on yNa+ = 7±(NaCl). It may be observed

that the experimental points lie below the theoretical curves at high

ionic strengths, whereas they fell above the curves in Figure 2. This

behavior suggests an error caused by the residual liquid-junction potential

which, as shown by Equations (10) and (11), has opposite effects on the experimental values of pCl and pNa, raising one and lowering the other. C. Calcium-Selective Electrode

The response of a calcium-selecdve electrode of the liquid

ion-exchanger type (Orion Research, Inc., Model 92-20) was studied in

Na(g/) I NaCl,CaCl2(/=/.^)) | AgCl;Ag
ACTIVITY STANDARDS 207

0.4

+^0.2

CP

? 0

0.2

log I

Figure 4. "Experimentar' values (circles) of -log yNa+. derived from emf measurements

with the sodium glass electrode and a calomel reference electrode, compared with values

defined by three conventions. a cell without liquid junction of this following type:

Caisel) I CaCl2(/) | AgCl;Ag

The cell was standardized at / = 0.0 1 , using the known activity coefficient

of calcium chloride at this molality [14]. The mean activity coefficients

of calcium chloride at 25 °C obtained experimentally are plotted in Figure 5 as a function of ionic strength (I). The curve is again drawn

through the mean activity coefficients obtained by other thermodynamic

methods and recorded in the literature [13]. The agreement is quite

satisfactory, confirming the accuracy of the response of the calcium elec- trode in solutions of calcium chloride. In order to examine the response of the calcium-selective electrode in mixtures of sodium chloride and calcium chloride, emf measurements of

this same cell with aqueous salt mixtures of a total molality of 1.0 mol

kg~^ were made. Poor reproducibility was observed, especially in solu- tions of high sodium content. This result suggests that the selectivity ratio Ca2+/Na+ is not sufficiently high for this particular application of the cal- cium electrode. In calcium chloride solutions at 25 XI, however, the

calcium-selective electrode was found to be reproducible to 0.2 to 0.3 mV

(0.01 pCa unit) and to reach equilibrium in about 1 min after immersion in the solution.
208 ION-SELECTIVE ELECTRODES

I \ \ \ I -3 -2 -I 0

log I

Figure 5. Determination of -log ycach with a calcium-selective electrode in a cell without

liquid junction. The curve is drawn through the accepted literature values. The response of the calcium-selective electrode in calcium chloride

solutions was also explored by measurements of a pCa cell with a satu- rated calomel reference electrode and a liquid junction. The cell was

standardized as before at / = 0.01. The results are shown in Figure 6,

where — log yca2+, that is, pCa+log mca2+, is plotted as a function of the

logarithm of the ionic strength. Once again, curve 1 was calculated by the

convention proposed here, curve 2 by the Maclnnes convention, and

curve 3 by assuming the z- relationship embodied in the Debye-Hiickel

formula, which leads to yca^+ = y±{CaCU). Curve 4 resulted from setting

7ca2+ equal to the mean activity coefficient of calcium chloride, as suggested by Shatkay [lOJ. As expected, curve 4 differs considerably

from those curves that are consistent with the Debye-Hiickel theory.

D. Fluoride-Selective Electrode

The accuracy of the response of a sodium-selective electrode having

been affirmed, this electrode was used in combination with the

fluoride-selective electrode, (Orion Research, Inc., Model 94-09) of the

solid-state (lanthanum fluoride) type, to study the response of the fluoride

electrode in solutions of sodium fluoride at 25 °C. The cell did not have a

liquid junction; it is represented as follows:

Na(^/) I NaF(m) | F{sel)
ACTIVITY STANDARDS 209

-3 -2 -I 0

log rriNaF

Figure 7. Determination of -log yNaF with a sodium glass electrode and a fluoride-selective electrode in a cell without liquid junction. The curve is drawn through accepted literature values. The cell was standardized in a solution of NaF of molality 0.01 mol kg~^

The results are shown in Figure 7, where the curve is drawn once again

through the known activity coefficients of sodium fluoride in its aqueous
210 ION-SELECTIVE ELECTRODES

solutions. The response of the fluoride electrode over a considerable

range of sodium fluoride concentration seems to be very satisfactory.

From a limited number of measurements, it appeared that the reproducibility of the fluoride-selective electrode is 0.2 to 0.3 mV (0.005 pF unit)

in solutions of sodium fluoride. Experimental values of the activity coefficient of fluoride ion, derived

from pF measurements in the cell with liquid junction, are shown as cir- cles in Figure 8. Curve 1 again represents the convention proposed in this

-3 -2 -I 0

log I

Figure 8. "Experimental" values (circles) of -log yr< derived from emf measurements

with a fluoride-selective electrode and a calomel reference electrode, compared with

values defined by three conventions. paper, curve 2 is derived from the Maclnnes convention, and curve 3 is based on the Debye-Huckel convention yF- = y±(NaF). Contrary to the situation with chloride ion illustrated in Figure 2, the experimental

points in Figure 8 fall below the curves at / = 1. This is probably because

sodium fluoride is incompletely dissociated at this high concentration.

The mean activity coefficient is therefore low and the conventional -log

7f- is too high. For the same reason, the points lie closer to curve 3 than to curves 1 or 2. VIII. Limitations of Practical pA Measurements

It is evident that the practical application of ion-selective electrodes is successful only when certain conditions are met. First of all, the response
ACTIVITY STANDARDS 211

of the electrode to changes in the activity of the ion to which it is selective

must be demonstrated, over the range in which the electrode is to be used,

by suitable measurements in a cell without liquid junction in the manner

outlined in earlier sections. Secondly, there must be assurance that other

ions that may interfere with this response are not present in sufficient concentration to affect the results. Finally, the experimental conditions must

be such that the residual liquid-junction potential error will be small rela- tive to the required accuracy of the measured pA.

We have seen in earlier sections that the response of the four types of

electrodes studied here is excellent over a range of at least three decades

of concentration. A listing of the chief interferences can usually be found

in the literature provided by the manufacturer of the electrodes. In

general, interferences are likely to be more serious with electrodes of the

liquid ion-exchanger type than with the solid-state type of electrode.

Glass electrodes designed for the measurement of cation activities usually

have a marked response to hydrogen ion, and therefore the pH of the

solutions under study may have to be controlled at values 3 or 4 units

higher than pA. Furthermore, sodium aluminum silicate glasses often

show a strong response to silver ion [17].

The uncompensated liquid-junction potential may cause some of the

most serious errors encountered in the experimental pA measurement. As

shown by Equation (14), the residual liquid-junction potential (expressed

in pA units) is defined as the difference between the measured operational

pA value and the defined — log for the same solution. It may therefore

be estimated from plots such as those of Figures 2, 4, 6, and 8, representing the difference between the experimental points (circles) and the solid curve labeled 1. Table 4 summarizes these approximate values of AEj

when the cell had been standardized in each case at an ionic strength of

0.01 in a pure aqueous solution of the salt concerned (sodium chloride,

calcium chloride, or sodium fluoride). In deriving the data given in the ta- ble, it was assumed that sodium fluoride (like the other salts) is completely dissociated at molalities up to 1 .0 mol kg ^ The influence of the composition and concentration of the solution on

the liquid-junction potential error is shown in Figure 9 (AEj of 3 mV cor- responds to AEj of 0.05 unit). The cell consisted of a silver-silver chloride

electrode used in conjunction with the saturated calomel electrode.

It was standardized in a sodium chloride solution of molality 0.01 mol and all of the measurements were made at 25 °C. The "true"

activity coefficients of chloride ion in each of the four salt solutions or aqueous salt mixtures were calculated by Equation (15). It is seen that the

variation of the liquid-junction potential error with ionic strength is about

the same for all four types of solutions, but for the solutions of calcium

chloride and the two mixtures it is 1 to 2 mV different from that for pure
212 ION-SELECTIVE ELECTRODES

6mV

•3mV

6mV

INFLUENCE OF AE; ON pCI MEASUREMENTS

NaCI

NaCI / KNO^(hl)

CaCl2

NaCI / KCI (hi)

log I 0

Figure 9. Residual liquid-junction potentials in a cell with a chloride-selective electrode and a calomel reference electrode for four types of solutions. The cell was standardized

in 0.01 m sodium chloride. solutions of sodium chloride. The corresponding error of 0.02 to 0.04 pCl

unit could be eliminated only by standardizing the cell in a solution containing the same salt or salt mixture as is present in the "unknown" solutions. On the other hand, an error of about 4 mV (0.07 pCl unit) is incurred

when the cell is standardized in 0.01m sodium chloride and used for measurements in solutions of the same salt at a molality of 1 .0 mol kg-^. These

estimates are consistent with calculated liquid-junction potentials [18].

To eliminate this concentration effect on the liquid-junction potential, it would be necessary to have a series of standard solutions of concentrations spaced over the entire range in which the electrode gives useful

results. For example, if the electrode were standardized in 0.5m sodium

chloride, the error in 1.0m sodium chloride would be reduced to about 1 mV (0.017 pCl unit).

Further measurements of electrode responses and residual liquid-junction potentials will be necessary before ideal standardization procedures can be recommended. It is nonetheless possible at the present time to sug- gest certain general procedures that promise to increase the accuracy of

routine pA measurements. These are:

1 . The pretreatment of the electrode should be identical for both the

"unknown" measurement and the standardization. (Soaking in distilled water for a few minutes and drying with soft absorbent tissue constitutes a satisfactory pretreatment.)
ACTIVITY STANDARDS 213

Table 4. Residual liquid—junction potential errors , AE^.

in practical pA cells standardized at / = 0.01.

/ AE

Cell: Na(^/) | NaCl (/) || KCKsat) | Hg2Cl2;Hg

0.001 0.01 pNa unit

0.01 (0) 0.1 -0.02

1.0 -0.07

Cell: C\{scl) I NaCl (/) |i KCKsat) | Hg2Cl2;Hg

0.001 -0.01 pCl unit

0.01 (0) 0.1 0.02

1.0 0.07

Cell: Fisel) \ NaF (/) || KCKsat) i Hg2Cl2;Hg

0.0001 0 pF unit 0.001 0

0.01 (0) 0.1 -0.02

1.0 -0. 10

Cell: Ca(.s6>/) | CaCl2 (/) || KCKsat) 1 Hg2Cl2;Hg

0.001 -O.lOpCaunit

0.01 (0) 0.1 -0.03

1.0 -0.22
214 ION-SELECTIVE ELECTRODES

2. Stirring conditions should be identical in both the measurement and

the standardization.

3. The same length of time should be allowed for equilibrium in the

"unknown" measurement as in the standardization. (The time interval

should be at least 2 min, but 5 to 10 min may be necessary for the most

reproducible results.)

4. Standardization with two standard solutions bracketing the pA of

the ''unknown" solutions is desirable. (This procedure diminishes errors introduced by non-theoretical electrode response and by the residual

liquid-junction potential.) IX. Acknowledgment

The authors are grateful to the Foxboro Company for support of the initial stages of this work.

X. References

[ 1 ] Van Rysselberghe. P.,Electrochim. Acta 9. 1 343 ( 1 964).

[2] Kortum, G., Treatise on Electrochemistry, 2nd ed.. Elsevier Publishing Co.. Amsterdam, 1965,Chapt. 8. [3] Manual of Physicochemical Symbols and Terminology, Commission on Symbols,

Units, and Terminology, International Union of Pure and Applied Chemistry,

revised version, 1968.

[4] Bates, R. G., Determination of pH, John Wiley and Sons, Inc., New York, N. Y., 1964,Chapts. 3 and 4. [5] Smith, E. R.,and Bates, R. G.,Compt. Rend. 15"" Conf. lUPAC, 1 18 (1949).

[6] Bates, R. G., and Guggenheim, E. A., Pure Appl. Chem. 1, 163 (i960).

[7] Maclnnes, D. A.,J. Amer. Chem. Soc.41, 1086(1919).

[8] Garrels, R. M., in Glass Electrodes for Hydrogen and Other Cations, G. Eisenman,

Ed., Marcel Dekker, Inc., New York, N. Y., 1967,Chapt. 13. [9] Butler, J. N., J. Appl. Physiol, (in press). [10] Shatkay, A., Anal. Chem. 39, 1056(1967).

[11] Harned, U.S., and Nims, L. F., J. Amer. Chem. Soc. 54, 423 ( 1 932). [12] Brown, A. S.,and Maclnnes, D. A., J. Amer. Chem. Soc. 57, 1356(1935).

[13] Robinson, R. A., and Stokes, R. H.. Electrolyte Solutions. 2nd ed., Butterworths, London, 1 959, Appendix 8. 1 0. [14] Shedlovsky,T.,and Maclnnes, D. A., J. Amer. Chem. Soc. 59, 503 ( 1 937). [15] Robinson, R. A., Trans. Faraday Soc. 36, 735 ( 1 940). [16] Robinson, R. A., and Bower, V. E.,J. Res. Nat. Bur. Stand. A70, 3 1 3 (1966). [17] Eisenman, G., in Glass Electrodes for Hydrogen and Other Cations, G. Eisenman,

Ed., Marcel Dekker, Inc., New York, N. Y., 1 967, Chapt. 9.

[ 1 8] Shatkay, A., Anal. Chem. (in press).
CHAPTER 7

STUDIES WITH ION-EXCHANGE CALCIUM

ELECTRODES IN BIOLOGICAL FLUIDS:

SOME APPLICATIONS IN BIOMEDICAL

RESEARCH AND CLINICAL MEDICINE

Edward W. Moore

Metabolic and Gastrointestinal Research Unit

Lemuel Shattuck Hospital

Commonwealth ofMassachusetts

Departments ofMedicine and Physiology

Tufts University Medical School

Boston, Massachusetts

I. Introduction

About four years ago I was preparing a chapter for Eisenman's book

on cation-selective glass electrodes [1]. In the summary of that chapter it was stated: "It would seem that such electrodes have opened

a veritable 'Pandora's Box' for investigators in the biological sciences.

The specific studies which can be effected by this new methodologic

tool will depend on the ingenuity of investigators and on improved

fabrication of both macro- and microelectrodes with high specificity

for specific ions. Electrodes with divalent-ion sensitivity will be of

particular interest." Having spent the previous four years in search

of calcium electrodes suitable for measurements in biologic fluids, we

(like so many before us) had become rather pessimistic about the

prospects for workable divalent-ion electrodes.

Only a few months later, however, we obtained from Orion Research,

Inc., the first ion-exchange electrode with high specificity for calcium ion

and began testing it in various biologic fluids. The present chapter will be concerned with some of the results obtained in our laboratory during

the past four years with these and subsequent ''generation" calciumion electrodes. Except for several abstracts and some preliminary

data presented three years ago at a symposium on bioelectrodes [2],

the data to be presented here have not been published previously.

The reason for this is that we have felt it absolutely essential to. have

extensive data in several biologic systems and under pathologic as

well as normal conditions before recommending general usage of these

electrodes. It is now quite clear that the calcium-ion electrode is providing

a powerful new tool in biomedical research and also in clinical medicine;

its potential usefulness is very great indeed.

At the outset it should be pointed out, however, that since these elec- 215
216 ION-SELECTIVE ELECTRODES

trodes have become commercially available, the response of biological in- vestigators who have tried them has varied from great enthusiasm to considerable dismay. Much of the disillusionment is probably due to the fact that the first commercial version of the electrode (Orion Research, Model

92-20) did not work satisfactorily in serum, a problem related to the

presence of protein and to the specific membrane used in that electrode. While this problem was subsequently resolved in the Orion flow-through

system, the fabrication of the latter electrode requires a certain amount of

skill and practice.

A. Physiologic Importance of Calcium

The physiologic importance of calcium is broad and complex. Classical

frog heart experiments of McLean and Hastings [3-5] 35 years ago

clearly demonstrated that ionized calcium, Ca++, is the physiologically active species, and a large number of important physiologic processes are now known to be critically dependent on calcium ion activity (or concentration). These include: bone formation and resorption, nerve conduction,

muscle contraction, cardiac conduction and contraction, cerebral function, renal tubular function, intestinal secretion and absorption, blood

coagulation, membrane and capillary permeability, enzyme function and

hormonal release from various endocrine glands. Great interest is cur- rently focused on two particular hormones with calcium ion regulatory

functions: 1) parathyroid hormone (parathormone) and 2) thyrocalcitonin

(calcitonin) of the parafollicular cells of the thyroid gland. There is little doubt that Ca++ is one of the most important electrolytes in human

physiology.

One of the greatest difficulties in both physiological and physiochemical studies of calcium metabolism has been the lack of a practical method

for the direct determination of ionized calcium. The development by Ross

[6] of ion-exchange calcium electrodes with high specificity for Ca++ al- lows study of numerous problems which would otherwise be quite dif- ficult or impossible.

B. Some Historical Notes

Previous attempts at electrode measurements of calcium ion activity in biologic fluids have been largely unsuccessful. Early studies with calcium

amalgam electrodes by Fosbinder [7] showed that such electrodes were

reliable only in aqueous solutions of calcium salts; the electrodes were

poisoned by very small amounts of protein, presumably due to formation

of a protein film on the metallic surface. Joseph [8] subsequently inter- posed a cellophane membrane between such electrodes and various
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 217

protein solutions. As noted by Greenberg [9], these measurements gave

only changes in activity coefficients of the salt caused by altered solvent

properties in the presence of protein. In recent years, investigators have

therefore turned to other types of electrodes. In the 1940's Sollner and coworkers [10-12] developed collodion

membrane electrodes for measurement of several ions, a technique later worked out in detail by Gregor and Sollner [13]. Studies of particular

physiologic note with this type of electrode were those of Carr [14]

which we shall refer to later. The difficulty with these electrodes was that other ions gave rise to potentials across the membrane, the electrodes

behaving reversibly to a given ion when only that ion was present. More

recently, multilayer membrane electrodes with selectivity for Ca++

have been carefully studied by Gregor and associates [15].

Following Eisenman, Rudin and Casby's [16] development of

sodium-selective glass electrodes, there was hope for a time that a glass

electrode could be perfected suitable for Ca++ measurements in biologic

fluids. Again, some success was achieved in pure aqueous solutions, as recently noted by Truesdell and Christ [17], but little or no success was

achieved in biologic fluids. The selectivity of glass electrodes developed

to date for Ca++ is probably too low for accurate measurements in biologic systems.

Of all the methods developed to date for measuring Ca++, the one most

widely used in biologic fluids is probably that using metal ion indicators,

particularly ammonium purpurate (murexide) [18-21]. There are several

restrictions with this method, however, including the necessity for removing proteins {i.e., precipitation, ultrafiltration, dialysis) and heavy metals

prior to analysis.

To quote Neuman and Neuman [22]: "We can say, however, without

fear of contradiction, that whoever develops a simple, accurate method

for the estimation of calcium ion activities will truly be a hero to clinician and researcher alike."

C. Interest in Serum Ionized Calcium

Since much of the following presentation will be concerned with elec- trode measurements in serum, it is reasonable to ask: Why are we particularly interested in serum ionized calcium? I believe the answer is apparent

from the model shown in Figure 1. According to this model, Ca++ in serum {via interstitial fluid Ca++) is in a state of dynamic interaction with

the interface calcium of bone and cartilage. Parathyroid hormone, through

mechanisms not fully understood, has bone-resorbing effects, with libera- tion of calcium to the extracellular pool, while calcitonin appears to have
218 ION-SELECTIVE ELECTRODES

INTESTINE KIDNEY

SERUM CALCIUM

Figure 1 . A model for the interactions of serum ionized calcium. an opposite effect.' Absorption of calcium from the intestine is influenced

by dietary intake and is enhanced by both Vitamin D and parathormone.

Excretion of calcium occurs by both urinary and fecal routes. Parathor- mone reduces renal tubular reabsorption of phosphate and, despite

enhanced proximal tubular reabsorption of calcium, results in an in- creased excretion of both calcium and phosphate [24-26].

Finally, Ca^+ of serum is in a state of dynamic interaction ("equilibrium") with the plasma proteins and various anionic ligands in serum. In 1911, Rona and Takahashi [27] found from dialysis experiments that serum total calcium represents both diffusible and non-diffusible fractions. Numerous studies [19-22, 28-40] have subsequently shown that there are three distinct calcium fractions in normal serum: 1) non-diffusible (protein-bound) calcium, CaProt, which, depending on pH and temperature, represents about 30-55 percent of the total; 2) diffusible,

non-ionized calcium (complexes and chelates), CaR, comprising some

5-10 percent of the total; and 3) ionized calcium, Ca++

In normal man, serum Ca++ and total calcium concentrations are maintained within rather narrow limits (about ± 10 percent). Whether this is af- fected primarily by actions of parathormone on kidney or on bone is a

subject of some controversy at the present time. In any case, it is evident

from Figure 1 that calcium ion in serum plays a very central role in the

overall scheme of calcium metabolism.

'The importance of calcitonin as a regulator of serum Ca++ in man has not yet been clearly defined, although it appears to be of considerable importance in certain lower

species such as fish, which often live in a high-calcium environment. As another

link between man and the primordial ocean, it is therefore of interest that the parathyroid glands first appear phylogenetically in amphibians. The reader is referred to a recent review on calcitonin by Copp [23].
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 219

II. Electrode Characteristics and Analytical Techniques

Two types of electrodes have been employed: 1) "static" or "membrane" electrodes, i.e., without sample-flow through the electrode, and 2)

"flow-through" electrodes.

A. Static-Type Electrode

A diagram of the "first generation" static electrode is shown in Figure

2. This electrode was prepared in the laboratory as follows: glass or CALCIUM ELECTRODE

TO

SHIELDED

CABLE

POLYETHYLENE

SHELL —

.

ELECTRO

METER

ION-EXCHANGE

RESIN

RUBBER

SEAL

SILVER WIRE

SORBITOLCaClj BULB

VISCOSE

MEMBRANE

K 1.3 cm >|

Figure 2. Static-type calcium electrode, prepared in the laboratory. plastic tubes were sealed at one end with Viscose dialysis tubing, held in place by a silicone rubber sleeve. The tube was then filled with 2-3 ml of

348-381 0-69— 16
220 ION-SELECTIVE ELECTRODES

a liquid ion-exchanger composed of the calcium salt of didecyl phosphoric

acid dissolved in didecylphenyl phosphonate, obtained from Orion

Research, Inc. (Cambridge, Mass.). Electrical contact was made with a chloridized silver wire coated with a solution of O.IM KCl or CaCU in fused sorbital. The volume of sample required was about 3 ml, and

equilibrium time was usually 1-3 minutes. Average life-span of these

electrodes was about 3 weeks. This electrode, which worked quite well in serum, is not to be confused with the "second generation" static elec- trodes marketed by Orion Research (Model 92-20), which employed a

Millipore rather than cellulose membrane and did not work satisfactorily

in serum. Another version of such "static" electrodes has been marketed

by Corning Glass Works (Corning, N. Y.), but we have not had ex- perience with this electrode.

Figure 3. Plexiglass CO2 chamber for Ca++ measurements with static-type electrodes. Both [Ca++] and pH are continuously monitored with separate electrometers. The cal- cium electrode (A) and pH electrode (B) are introduced into a standard or test solution with a calomel half-cell (C) as common reference electrode. Continuous stirring is achieved by a magnetic stirrer. Sample is maintained at 37 °C by circulating water (D). Additional samples may be pre-warmed (E). Air temperature is maintained at 37 °C by a

light bulb (F) connected to a rheostat. Water and air temperatures are monitored by

thermometers (G) and (H), while (J) is the thermoregulator control box. Sample pH is varied by alteration in chamber pCOz.
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 221

The static electrode, while being rather crude, had the distinct ad- vantage of allowing direct study of pH effects on ionized calcium. This

required the construction of a suitable Plexiglass CO2 chamber, shown in Figure 3, in which pCOz and sample pH could be carefully controlled.

Both ionized calcium and pH were continuously monitored through

separate electrometers, using a calomel half-cell as common reference.

Continuous stirring was achieved by a magnetic staTer, and both water

and air temperature were maintained at 37 °C. Virtually instantaneous

changes in sample pH could be achieved by variation in chamber pCOi.

Because of the pH dependency of ionized calcium, all values given subsequently for the static electrode are those at the original whole blood pH.

B. Flow-Through Electrode

The "third generation" electrode, and the second type to be used in the

present studies, was a flow-through electrode marketed by Orion

Research, Inc. (Model 98-20), shown diagrammatically in Figure 4. Electrometer

Ag/AgCI Wire

Internal Reference Solution

Organic Exchanger

Porous Membrane

:}rr--Sat. KCI

Calomel Electrode

Sample Chamber

Syringe

Pump

-Sample

Figure 4. Diagram of a flow-through electrode obtained from Orion Research, Inc. (Cambridge, Mass.). This electrode became available about two years after the static elec- trode studies had begun. The sample flows through the electrode chamber

at about 0.05 ml/min, using a gear-driven syringe pump. All measure- ments with this electrode were made at 25 °C. The flow-through system has several advantages over static-type elec- trodes: 1 ) equilibration time is quite rapid, usually 30-60 seconds; 2) it is
222 ION-SELECTIVE ELECTRODES

more stable, with typical drift of 2-5 mV during the course of a day, as compared with 3-lOmV/day with static electrodes; 3) less sample

volume is required, several measurements being possible with a 1 ml sample; 4) the measurement is anaerobic, analogous to a blood pH measurement. We now use only this type of electrode in our laboratory, but it should

be noted that it has two disadvantages: 1) pH effects on ionized calcium,

to be described below, cannot be directly monitored, as is readily done

with the static-type electrode; and 2) it has not yet been thermostated, so

that measurements are most conveniently made at room temperature.

Since the binding of calcium to serum proteins is both temperature and

pH dependent, some difference between serum [Ca++] at 37 °C (static

electrode) and 25 °C (flow-through electrode) would be expected. This

difference will be noted below in studies of sera from normal subjects.

For a perfect electrode, sensitive to only one ion species, the electrode

potential, £, is given by the Nernst equation:

where a is the activity of the cation or anion being measured, E° is a constant and R, T, n and F are the gas constant, absolute temperature,

number of transferred electrons and the faraday constant, respectively. In actual practice, no glass or ion-exchange electrode behaves perfectly, inasmuch as all electrodes will respond to more than one species

(as illustrated by the so-called "alkaline error" or "sodium error" for glass

pH electrodes at high pH). Thus, one is necessarily concerned with the

"selectivity" of a given electrode, i.e., the potential which will be gen- erated by one ion species in preference to other ion species. In their work with sodium-selective glass electrodes, Eisenman. Rudin

and Casby [16] developed the following empirical equation to describe

electrode potentials in mixtures of two univalent cations:

C. Electrode Selectivity

•2.3RT

nF

logfif (1)

E = E°^ 2.3 RT

nF log [(A+)^'"ab+A'1'j^'ab(B^)'/"ab]"ab (2)

where (A+) and (B+) are the activities of ions A and B, respectively, and

/cab and /7ab are adjustable parameters which are constant for a given elec- trode and cation pair. The selectivity constant (A^b) denotes how well the
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 223

electrode "sees" one cation {A+) in preference to the other cation (B+).

Ross [6] has found that the potential of ion-exchange calcium elec- trodes is similarly given by the empirical equation:

where A, and Zi are the activity and charge of an interfering ion /. As shown in Table 1 , the major interfering ions of concern in serum and

other extracellular fluids are Na+ and Mg++. The selectivity for Ca++ over Na+ (and also K+) is so high that precise selectivity measurements are

rather difficult to obtain. Ross [6] has found A^aNa and kcaMn values of

10"^ and 0.014, respectively. Similar results have been obtained in our

laboratory [2]. Thus, in serum containing ImM Ca+ + , the presence of

\50mM Na+ would result in approximately 1-2 percent enhancement of

apparent calcium ion concentration. The presence of 0.5mM Mg+ + in serum would also yield an error of about +1 percent. Overall Na+ and

Mg++ error is thus believed to be about +2 percent. Hydrogen ion and

K+ errors must be considered in gastric juice and intracellular fluids respectively, but are of no consequence in extracellular fluids. The elec- trodes have been found to be unresponsive to anions and to chelates of

calcium, and are thus highly specific for calcium ion. Below a pH of about

5.5, the electrodes no longer show Ca++ selectivity but behave as pH

electrodes [6]. We have obtained very reproducible [Ca+ +

] values in gastric juice, however, following alkalinization to pH 6-7 with NaOH [41].

Table 1. Selectivity constants (ki) of ion-exchange calcium

electrodes with respect to principal cations in extracellular (ECF) and intracellular (ICF) fluids.

E= constant +

2.3 RT

riF log (3)

E = constant +

2.3 RT

nF

[A,]

Ratio:

[Ca+i

CaA . Ion (approximate) Serum and ECF ICF

Na 10,000/1 150 10-15

10,000/1 4-5 150

Mg^^ 100/1

> pH 6

0.5-1 1.5-20

10-^ 10-^
224 ION-SELECTIVE ELECTRODES

D. Electrode Calibration

Neglecting the effects of other cations, the observed electrode potential

is a function of calcium ion activity (Ca++). According to the Nernst equation, a 10-fold change in (Ca++) should yield a potential change of

30.8 mV at 37 °C and 29.6 mV at 25 °C. These theoretical slopes have

been observed occasionally; more typical values have been about

29 mV and 27 mV, respectively. Electrode response has been found to be linear over the Ca++ concentration range 1.0-lOmM. Since the entire

standard curve may shift several millivolts during the course of a day,

possible errors resulting from such drift were minimized in the present

studies by calibration in standard solutions before and after each un- known solution.

While electrode response is a function of calcium ion activity, the ab- solute value of this activity in any given solution is uncertain since in- dividual ion activity coefficients cannot be experimentally determined.

Using a Na-electrode, Ag-AgCl electrode system, Moore and Ross [42]

have estimated ycach iri mixed CaCl2-NaCl solutions to be about 0.54

when NaCl = 0. 15M. The development of a Ca++ activity scale by

Bates, reported in this volume, represents an important advance in the application of calcium electrodes to biologic investigations. In the following studies, all Ca^+ values will be given in concentration

terms, [Ca++], relative to mixed CaCU-NaCl standard solutions with

total ionic strength nearjthat of serum, i.e., — 0.1 6M. In so doing, it is as- sumed that yca++ is similar in standard and unknown solutions. This

assumption is probably reasonable, since activity coefficients are primarily related to total ionic strength [ 1 ,42-44].

Electrodes were therefore calibrated with solutions containing 150mM

NaCl and 0.5-lO.OmM CaCb; ionic strength thus varied from 151.5mM

to 180mA/. The fact that electrode response was linearly related to concentration over the indicated range suggests that yca++ similar

in the different solutions, in accordance with Harned's rule [1,45].

The pH of these standards varied from about pH 6.0-7.0; no buffers were employed because: (1) the buffer would have uncertain effects on Ca+^ activity, and (2) there is, as noted above, no detectable error with these electrodes above about pH 5.5. We would therefore suggest

that buffers not be employed unless their possible effects on (Ca+^) are studied specifically. (For example, both bicarbonate and phosphate form

calcium complexes, as will be noted later.) Neglecting the effect of other cations on the electrode potential, the

potentials in unknown and standard solutions are given by:

^unk = ^° + 51og(Ca^ + )unk (4a)

£° + Sl()g([Ca + ^]-7Ca^^)unk (4b)
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 225

^3td-^^° + S log ( [Ca++] •yca^+)std (4c)

where S is the Nernst slope factor; 2.3 RT/nF. Assuming

UtlK std the potential difference, AE, between unknown and standard is given by:

M^l / [Ca^"]unk\

S '""^UCa^+lstd/ (5a)

(or)

[Ca^^]unk-^[Ca-"]std-10^^/^ (5b)

While Equation (5) is easily solved graphically, we have found it convenient to record AE directly with an IBM Selectronic typewriter using

a suitable interfacing device between the electrometer (Orion 801 digital

pH meter) and typewriter. [Ca++]unk is then obtained by manually feeding

AE into an Olivetti-Underwood Programma 101 computer, with direct

printout of [Ca++]unk- The entire operation takes 10-15 seconds and is somewhat more accurate than graphical interpolation.

Although it is implicit in Equation (5), it should be emphasized that small errors in electrode potential measurements may yield rather large errors in estimated [Ca++] in unknown solutions. Thus, with an electrode

slope of 28 mV, an error of 1 mV in measured potential at 25 °C would

yield about an 8 percent error in apparent [Ca++].

All potential measurements with static-type electrodes, in both stan- dards and unknowns, were made at 37 °C in a Plexiglass chamber (Fig.

3), in which sample pH was varied by alteration in /7CO2. Electrode

potentials were monitored with either a Corning Model 12 pH meter

(Corning Scientific Instruments, Medfield, Mass.) or Orion Model 801

digital pH meter. Ionized calcium measurements in each serum, whole

blood and ultrafiltrate were made over the pH range 6.8 to 7.8. This

resulting curve was bracketed by standard curves obtained in CaCb-NaCl solutions. Duplicate measurements were similarly made.

Because of the pH dependency of ionized calcium levels in sera and ul- trafiltrates, all [Ca++] values given subsequently for the static electrode

are those at the original whole blood pH. In the flow-through electrode

studies, [Ca++] was either determined immediately (anaerobically at 25

±2 °C) or in samples frozen under oil, reequilibrated with 5 percent CO2

prior to analysis.

It should be emphasized that no pH effect on [Ca++] was observed in standard solutions.
226 ION-SELECTIVE ELECTRODES

E. Ultrafiltration and Other Methods

Ultrafiltrates of sera were obtained at 25±2°C with a high-pressure

dialysis cell obtained from National Instrument Laboratories (Rockville,

Md.) shown in Figure 5. Viscose (Union Carbide Co.) dialysis tubing with an approximate mean

pore diameter of 25A was used in all experiments and was soaked in running water and then distilled water for about 20 minutes prior to use. After insertion of the dialysis tubing, the chamber was well-aerated with

5 percent CO2. Serum ( 1 0 ml), which had been separated under oil and its pH determined, was then introduced anaerobically into the Viscose bag

and pressure applied with pure nitrogen gas at 4-45 psi (pounds per square

inch).

The rate of ultrafiltration, at given pressure, is a function of wetted bag

surface area and should thus decrease exponentially. This was found to be

the case. Preliminary studies showed that the average time required to reduce serum volume to one-half was about 10 hours at 4 psi and about 3 hours at 45 psi. In early studies of sera from normal subjects, it was found that ultrafil- trate pH was somewhat higher (0.1-0.2 pH units) than that of the original serum; the chamber was therefore modified to allow continuous gassing

with moisturized 5% CO2 during ultrafiltration. With this small modification, pH regulation was quite close; average ApH between ultrafiltrate and original serum in 9 normal and 10 pathologic sera was 0.039 ±

0.013(SE) units. After formation of 2-3 ml of ultrafiltrate, each sample was removed

anaerobically from the cell and immediately introduced into the Plexiglass

chamber (which had also been pre-aerated with 5% CO2) for electrode

analysis of ionized calcium. All ultrafiltrates were clear; occasional

cloudy samples were discarded and the experiment terminated.

Total calcium concentrations [Ca] were determined in duplicate by

EDTA titrafion in IM KOH using Cal-Red (K & K Chemicals, Plain- view, N. Y.) as indicator [20,46]. Twenty-five normal samples (20 sera,

5 ultrafiltrates) were also analyzed by atomic absorption (AAS) spec- troscopy (Model 290, Perkin-Elmer Corp., Norwalk, Conn.). A close cor- relation (r = 0.96) between EDTA (y) and AAS (x) values was observed

in both sera and ultrafiltrates; the two were related by the function: y =

0.16 + 0.96 X. Atomic absorption values thus averaged about 0.1 mM

lower than corresponding EDTA values in serum and about 0.06mM

lower in ultrafiltrates. Unless otherwise indicated, all subsequent values

will be those obtained by EDTA titration. Serum total protein was measured by the biuret method [47]; albumin and globulin were determined

by electrophoresis.
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 227

To

Nitrogen

Cylinder

A

[Ml

Figure 5. Ultrafiltration cell employed in ail studies. Viscose dialysis tubing is inserted

into a fritted stainless steel cylinder (A). The chamber is pre-aerated (C) with 5%C02,

95% O2; serum is then introduced at (D) into the dialysis tubing and pressure applied with pure nitrogen gas. Ultrafiltrate (E) collects between the steel cylinder and an outer

plastic jacket (B), and is removed without exposure to air by a syringe attached at (F). Not shown is a modification made to allow more precise pH regulation during ultrafiltration. This consisted of drilling a small hole in the outer jacket about 2 inches from

the bottom to allow egress of moisturized 5% CO2, introduced through the upper side arm

throughout ultrafiltration.
228 ION-SELECTIVE ELECTRODES

The following symbols and methods of calculation are used:

[Ca++] = electrode ionized calcium concentration (mMj

[Ca] = total calcium concentration (mMj

[Alb] = serum albumin concentration (g/1) [Glob] = serum globulin concentration (g/1) [CaProt] = concentration of calcium bound to serum proteins, calculated as the difference in serum [Ca] and ultrafiltrate [Ca]

(mMj

[CaR] = concentration of diffusible complexes and chelates of cal- cium (mM). [CaR] was calculated as the difference

in ultrafiltrate [Ca] and ultrafiltrate [Ca++], or in a few

instances, as the difference in ultrafiltrate [Ca] and serum

• [Ca-].

III. Results in Normal Subjects^

A. Do Ca++ Electrodes Work in Biologic Fluids?

There are several ways in which it can be shown that the calcium elec- trodes respond to changes .in ionized calcium levels. In protein-free solu- tions such as ultrafiltrates, this is indicated by quantitative recovery upon

addition of CaCl2-NaCl solution at constant total ionic strength. A

representative study is shown in Figure 6; virtually identical results were

obtained in 6 additional subjects. A quantitative linear increase in [Ca++] was observed in all studies. In serum, the "recovery" of added calcium is not quantitative because

of partial binding of added calcium to the serum proteins. This will be

developed more fully in Section IV below.

That the e'ectrodes respond specifically to ionized calcium has also been shown by using the electrodes as monitors or end-point detectors for chelating titrations. As shown in Figure 7, upon addition of an excess of

EDTA to serum or ultrafiltrate, there was a rapid decrease in ionized cal- cium, followed by a further decrease upon addition of NaOH. Virtually

identical results were obtained in 4 additional studies. Note that the

decline in [Ca++] in serum was less abrupt than in ultrafiltrate. Note

particularly that the residual [Ca++] value was quite small, suggesting that there was little or no extraneous potential in these fluids, i.e., of

non-Ca++ origin; the residual value of about 0.04mA/ probably reflects Na+ error in the electrode potential.

Another way of showing that the electrode responds to calcium ion is to measure the dissociation constant (/C^) of an important calcium

complex, such as calcium citrate. A single experiment, using the

flow-through electrode at 25 °C, was therefore performed as follows: to an aqueous solution containing l.OmM CaCb and 120mM NaCl, 0.1 ml

^ Preliminary reports of these studies have been published [2,48].
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 229

1.6-

1.4-

[Ca*1

mM

1.2

1.0-

0-"

ULTRAFILTRATE

(Subject N.D.)

/

/

^|:| REGRESSION

0.2 0.4

ADDED CALCIUM (mM)

06

Figure 6. Representative recovery study in an ultrafiltrate of serum from a normal subject. Pure CaClz (lO.OmM) was added serially (30 />il) to a 3.0 ml ultrafiltrate sample at constant pH (pH 7.37). Resulting abscissa values are expressed as mM concentration. The dashed line is the theoretical 1 : 1 regression.

increments of lO.OmM citric acid were serially added and the final pH ad- justed to 7.0 by addition of NaOH. Calculated total ionic strength for each solution was about 0.1 5M. With each serial addition of citrate,

[Ca++] was measured with the calcium ion electrode.

Results are shown in Figure 8. Upon 8 serial additions of citrate, there was a progressive decrease in observed [Ca++]. Corresponding total citrate concentrations, corrected for volume, varied from 0.20mM to 1.67mM. Values for Xcacu calculated for each point in the left-hand

side of Figure 8, varied from 0.332 to 0.453, with a mean of 0.398.

In negative log terms, this corresponds to p/C' values of 3.34 to 3.48. with a mean x^K' of 3.40. The ratio [CaCit]/[Cit ] as a function of pCa

is shown in the right-hand side of the figure.
230 ION-SELECTIVE ELECTRODES

1.2 r

I.I -

EDTA ADDED NaOH ADDED

PH

Figure 7. Effect of EDTA on ionized calcium concentrations in serum and ultrafiltrate as monitored with the static-type calcium electrode. 10 /xmoles (in 30 /xl) of di-sodium EDTA was added to 3.0 ml samples, yielding final EDTA concentrations of about 3.3 mM. Sample pH was then increased by addition of \M NaOH in 10-20 ^il increments. The value of 3.40 for pKcacn is somewhat higher than most reported

studies [49] in which, by various methods, pK' values of about 3.2 have been obtained at this ionic strength and temperature.

B. Serum Ionized vs. Total Calcium

Ionized and total calcium concentrations were measured in 91 sera from 60 normal subjects. Of these, 72 studies in 52 subjects were made

with static-type electrodes; the remainder were made with the more
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 23i

2.0-1

1.5-

[CaCit] I.0--

0.5- 02- pK'O.40

0 0

0 05 1.0 TOTAL CITRATE

(mM)

.5 3.0 3.2 3.4 3.6 -log (Ca**l

Figure 8. Determination of the dissociation constant of calcium citrate by serial addition of citrate to a ImM CaClz solution (25°C, pH 7.0, I =0.\5M).

recently obtained flow-through electrode. As shown in Figure 9, there was considerable variability in total serum calcium, with a range of 2.12

to 2.88mM [mean: 2.477 ± 0.286 (2 SD) mM]. Absolute variability in ionized calcium was only about one-half that of total calcium, with a range

of 0.94 to 1 .33mM. Percentage variability was thus similar for ionized and

total calcium. Overall mean serum ionized calcium concentration for both

static and flow-through electrodes was 1.1 36 ±0.126 (2 SD) mM. Thus,

95 percent of normal subjects would be expected to lie in the range:

l.OlmM to 1.26mM.

[Ca++] measurements were made in 1 1 subjects with both static-type

and flow-through electrodes, with an intervening period of 1 to 10

months. Mean values for the two electrodes were almost identical: 1.169

± 0.05 (2 SE) mM and 1.161 ± 0.012mM, respectively. For all studies

with the flow-through electrode (19 studies in 18 subjects), mean [Ca++] was 1 . 1 63 ± 0.0 1 4 (2 SE) mM, which was not significantly different from

the mean value of 1.127 ± 0.019 (2 SE) mM obtained with static-type

electrodes in 52 subjects.

As noted in Section II.B. above, small differences in mean [Ca++]

values for the 2 types of electrodes might be expected, due to pH and temperature effects. Thus, static electrode [Ca++] values were obtained at 37 °C and at the original whole blood pH; flow-through [Ca++] values were at 25 °C and at the pH of serum after separation under oil. For all studies, the arithmetic average of venous pH was 7.34 ±0.01 (2 SE)

while for separated serum it was 7.42 ± 0.01 (2 SE). Serum pH, when
232 ION-SELECTIVE ELECTRODES

TOTAL CALCIUM

(EDTA)

mM mgm/IOOmI

3.0t -rl2.0

2,5

2.0

.0-

0.5-

-10.0

Meant 2 SD

2.477± 0.286

mM

(n=70)

IONIZED CALCIUM

( Electrodes ) mM mgm/lOO ml

3.0-1 rl2.0

2.5-

8.0 2.0-

-6.0 1.5

4.0

2.0 0.5-

-8.0

Mean ± 2 SD

1.136 ± 0.126

mM

(n=70)

10.0

6.0

-4.0

2.0

Figure 9. Serum ionized and total calcium concentrations in 52 subjects studied with

static-type electrodes • and 18 subjects studied with flow-through electrodes O. Notice

the narrow range of ionized calcium values. The 95 percent confidence limits for the population are indicated by respective means ± 2SD:2. 1 9-2.76mM for total calcium and

1.0 1-1. 26mA/ for ionized calcium.
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 233

analyzed for [Ca++] with the flow-through electrode, thus averaged

0.08 pH units higher than blood pH. From observed pH effects on

[Ca++], (Fig. 11) this difference would be expected to yield [Ca++]

values with~the flow-through electrode about 3 percent lower than with

the static electrode. That the mean [Ca++] with the flow-through elec- trode was 0.04mM higher than with static electrodes probably reflects a temperature effect on the binding of calcium to serum proteins. Thus,

from ultracentrifugation studies of Loken et al. [37], free [Ca++]

in serum is about 5-6 percent higher at 25 °C than at 37 °C at this pH.

Since the pH and temperature effects are opposite in direction, [Ca++]

values with the flow-through electrode would thus be expected to be about 2-3 percent greater than with the static electrode, almost exactly

the difference observed.

In these 60 normal subjects, a finding of particular note was a complete

lack of correlation between serum ionized and total calcium concentrations, as shown in Figure 10. Ionized calcium was within a narrow range,

irrespective of the total calcium level. This finding is potentially of great

I.4-.

I.3H

1.2 [Ca+^]

nnM I I

LO0.9-

• •%>

^ :

• . \

• = static Electrode (52)

o= Flow-Through Electrode (18)

JL—1—

2.1 2.2 2.3 24 2.5 2.6 2.7 2.8

TOTAL CALCIUM CONCENTRATION

mM

I 2.6 —

1

2.9

Figure 10. Relation between ionized and total calcium concentrations in 52 subjects studied with static-type electrodes • and 18 subjects studied with flow-through elec- trodes O. Note the complete lack of correlation.

clinical importance since serum ionized calcium is the physiologically-active species, yet serum total calcium is measured routinely in hospitals

throughout the world. The discrepancy between serum ionized and total
234 ION-SELECTIVE ELECTRODES

calcium concentrations reflects variation in serum protein (mainly albu- min) concentrations. Thus, as will be noted in Section VI below, variation

in serum total calcium concentration in normal subjects was almost quantitatively accounted for by a corresponding variation in protein-bound cal- cium. In other words, it will be shown that a serum total calcium measure- ment in the normal is an indirect measurement of the serum albumin level. In an effort to determine the variability of serum ionized and total calci- um concentrations within a given individual, 39 studies were performed

in 15 subjects over a period of 2 years. The average interval between stu- dies was 7.6 months. The average difference between [Ca++] levels for each study was determined for each subject. For example, if [Ca++]

values of 1.10, 1.15, and 1.20mM were obtained in 3 studies, the average

difference between studies 1-2, 2-3 and 1-3 would be: 0.05 + 0.05 + 0.10 = 0.067 mM.

Ionized calcium concentrations were remarkably constant within a given individual. The average difference between replicate studies for the

15 subjects was 0.07 ± 0.03 (2 SE) mM. Since mean [Ca++] for the 39

studies was 1.13 ±0.01 (2 SE) mM, the average difference between re- peated studies was about 6 percent. Absolute variability in total serum

calcium was about three times as great as with ionized calcium: mean

total calcium for all studies was 2.52 ± 0.06 (2 SE) mM with an average

difference between repeated studies of 0.23 ± 0.06 (2 SE) mM.

As a practical clinical or research tool, the value of the electrodes

would be considerably enhanced if reliable measurements could be made

in samples previously frozen and stored. This was therefore investigated

early in the present studies (Table 2). Ionized calcium was measured in serum from 7 normal subjects before and after freezing for 24-72 hours.

No significant differences were observed. Upon freezing of ultrafiltrates,

however, a decrease in [Ca++] was frequently observed; some samples

became cloudy and occasional precipitates were noted. It is concluded

that [Ca++] may be reliably determined in previously frozen serum, but

not in ultrafiltrates previously frozen. The apparent lack of precipitation

in serum may reflect solubilizing properties of the serum proteins.

C. pH Effects on Ionized Calcium

Clinically, it has long been recognized that alkalosis may precipitate

hypocalcemic tetany. It is also known that the binding of calcium to serum proteins increases with increasing pH [35,37,39]. The static elec- trode and CO2 chamber have allowed, for the first time, a direct study of

such pH effects. In all studies with static electrodes (52 subjects), the ef-
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 235

Table 2. Effect of freezing on semm ionized calcium

concentration.

Ionized calcium concentration (mM)

Before After A

1. R.C. 1.15 1.16 +0.01

2. C.G. 1.15 1.17 +0.02

3. N.G. 1.06 1.06 0

4. S.K. 1.12 1.16 +0.04

5. N.L. 1.26 1.26 0

6. L.M. 1.16 1.20 +0.04

7. S.S. 1.19 1.19 0

Mean 1.155 1.171 +0.016

feet of pH on serum [Ca++] was investigated over the range pH 6.8 to pH

7.8. Similar studies were also made in ultrafiltrates from 16 normal subjects. A representative study in a single normal subject is shown in Figure 1 1

.

As expected, there was a pronounced pH effect in serum, with a linear or slightly sigmoid decrease in ionized calcium with increasing pH. The

4 curves represent duplicate runs, each duplicate being bracketed by stan- dard curves. (The maximum variability between duplicate serum measurements in Figure 1 1 corresponds to about 1 mV in measured potentials.) The pH effect presumably results from competition between Ca++

and H+ for negative sites on serum proteins and was considerably accentuated in residual ''bag serum" following ultrafiltration, i.e., upon concentration of the serum proteins. The pH effect was virtually instantaneous

and was completely reversible. In each of 16 subjects studied, a pH effect was also observed in serum ultrafiltrates, often almost identical to that in corresponding

sera, as in the subject shown in Figure 11. This was quite unexpected

and has since been studied rather extensively by Dr. Joel Jacknow in our

laboratory. We will return to this problem below, in considering the dif- fusible calcium complexes of serum. D. Components OF Serum Total Calcium

It is well-recognized that the total calcium concentration in serum

represents the sum of 3 distinct fractions: 1) protein-bound calcium

[CaProt], 2) diffusible calcium complexes [CaR], and 3) ionized calci- um [Ca++]. Total ultrafiltrable (diffusible) calcium, representing both

348-381 0-69— i7
236 ION-SELECTIVE ELECTRODES

(Subj. A D.)

"

1 1 1 1 1 1 ' 1 1 1 1 1 1

6.8 7.0 7.2 7.4 7.6 7.8 6.8 7.0 7.2 7.4 7.6 7.8 pH pH Figure 1 1. Ionized calcium concentration as a function of pH in serum, ultrafiltrate and

bag serum from a normal subject. In serum and ultrafiltrate. each [Ca++] curve was

bracketed by measurements in standard CaC^-NaCl solutions; the 4 curves therefore represent duplicate runs. (The range of variability corresponds to about ImV.) The 2 curves for bag serurn represent a single run bracketed by standards. Note that the mean

curves for serum and ultrafiltrate were virtually identical, while an accentuated pH effect was observed in residual bag serum, i.e., upon concentration of the serum proteins.

ionized and complexed calcium, has been widely used as an index of serum ionized calcium.

In the 16 subjects from whom ultrafiltrates were obtained, mean serum

[Ca] was 2.54 ± 0.04 (SE) mM and mean ultrafiltrate [Ca] was 1.52 ±

0.04mM. Average [CaProt] was thus 1.02mM and 59.6 percent of serum [Ca] was ultrafiltrable, a figure in general agreement with previous

studies [21,29-31,35,39,40]. Ionized calcium concentrations in sera and

ultrafiltrates were almost identical, with means of 1.16 and 1.1 7mM,

respectively. Mean [CaR] was 0.35 ± 0.03mM. Of the total ultrafiltrable calcium, the ionized fraction varied considerably (range: 66.7-90.2 per- cent) with a mean of 76.7 percent. Total ultrafiltrable calcium was thus not a reliable index of serum ionized calcium in normals. Resulting frac- tions of the serum total calcium are summarized in Figure 1 2.
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 237

mM mgm/IOOmI

[CaProtJ

[CoR]

[Ca++]

(n = l6)

Figure 12. Components of serum total calcium obtained from ultrafiltration data in 16 normal subjects. Indicated percentages are the mean values for the group.

E. Diffusible Calcium Complexes [CaR] of Normal Serum

In their studies with the frog heart, McLean and Hastings [4] found

0. 15-0.34mM of the serum total calcium could not be accounted for as [Ca++] or [CaProt]; similar results were later obtained by Morison

et al. [33]. Neuman and Neuman [22] have given 0.3mM as the estimated

value for the concentration of diffusible calcium complexes of normal

serum. More recent studies by Walser [21], however, have yielded

considerably lower values, about 0.1 6mM, using murexide for measure- ment of [Ca+ + ]. Rose and associates [19,50] have reported values

somewhat lower than those of Walser.

Our value of 0.35mM for [CaR] is therefore at least twice as high as

that obtained in recent studies. At least half of the difference, however,

may be related to the different chemical methods employed. Thus, if we
238 ION-SELECTIVE ELECTRODES

had used atomic absorption spectroscopy (AAS) for measuring total cal- cium, rather than EDTA, our [CaR] value would have been about

0.29mM (Section I I.E. above). Similarly, ultrafiltrate [Ca++] values re- ported for murexide are higher (0-0. 3mM) than those obtained here

with the electrode. This would yield [CaR] values proportionately lower

than those obtained from electrode data. This problem has been studied by Dr. Jacknow in our laboratory. His

results in 5 aqueous solutions, each containing 1.5mM CaCL and 150mM

NaCl, are shown in Table 3. Table 3. Complexed calcium in 5 aqueous solutions each containing

1.50 mM /I [Ca++] and 150 mM /I NaCl.

Solution . Free[Ca++] mM/1 Complexed [Ca++] mM /I Phosphate 1.48-1.50 0.00-0.02

1.0 mM

Lactate 1.48-1.49 0.01-0.02

1.0 mM

Citrate 1.41-1.43 0.07-0.09

0.12mM

Bicarbonate 1.34-1.37 0.13-0.16

25 mM

Mixture

Mean 1.27 0.25

Range 1.25-1.29 0.21-0.29

Solutions of phosphate, lactate, citrate and bicarbonate were each

prepared at the average concentration of these ions in normal serum, and

also a mixture of all of these ions. Resulting Ca++ and complex concentrations are indicated, the average sum of the complexes being 0.25mM.

Notice that about half the total was accounted for by bicarbonate.

At a Ca++ concentration of 1.1 5mM, i.e., the average value in normal

serum, the sum can be calculated to be about 0.2 ImM. This would there- fore appear to be the minimum value for [CaR] in serum, about O.OSmM

less than that observed by AAS in our normal subjects by ultrafiltration. While this difference may reflect ultrafiltration error, it would appear that a calcium sulfate complex must also be considered. Nakayama and

Rasnick [5 1 ] have recently obtained a K,; for CaS04 • 2H2O of 5.9 X 1 0-^. At a normal serum SO4 level of 0.5mM, a calcium sulfate complex of

about 0.08-0. 1 mM might be expected. This would be just enough to ac-
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 239

count for the difference between our ultrafiltration and pure solution

(Table 3) values. Why then was there a pH effect on Ca++ in serum ultrafiltrates? Calculations indicate that the dissociation of each of these complexes —

phosphate, lactate, citrate, and bicarbonate, should not vary with pH

over the pH range compatible with life and this was experimentally

confirmed by Dr. Jacknow in these solutions, i.e., no pH-effect was

observed. Calculations do indicate, however, that ultrafiltrates are probably supersaturated with calcium carbonate and perhaps also

hydroxy-apatite. While unmeasured pH-dependent polyelectrolytes may

also be present, we believe the observed pH effect in ultrafiltrates most

likely represents a kinetic problem related to variable precipitation of certain calcium complexes.

F. Whole Blood Ca++

Ionized calcium was determined in serum and in simultaneously-drawn

heparinized whole blood from 6 normal subjects (Fig. 13). pH effects on [Ca^^] in whole blood were roughly similar to those in corresponding

sera. In all cases, however, [Ca++] was less in whole blood than in serum

at normal venous pH (7.3-7.4). Although the average difference was small

(mean A = -0.045mM at pH 7.32), it was significant (p < 0.01).

1.2

0

-

1.4 -,

1.2-

1.0-

1.4 n

1.2

1.0-

0.8

08-

pH 68

Figure 13. Comparison of ionized calcium concentrations in serum • and heparinized whole blood x as a function of pH in 6 normal subjects. Note that below pH 7.6, whole

blood [Ca++] was less than corresponding serum [Ca' ] in all subjects.
240 ION-SELECTIVE ELECTRODES

G. Calcium-Heparin Complex

Because of the significant reduction in heparinized whole blood

[Ca"^+], the effects of heparin on [Ca++] were studied as follows: sodium

heparin ( 1 0,000 units per ml) was added in 0.02 ml increments to an aque- ous solution (1.0 ml) containing 5mM CaCL and 150mM NaCl, with con- tinuous monitoring of ionized calcium by the electrode. As shown in Figure 14, there was a progressive decrease in the observed ionized calci- um concentration, amounting to about 45 percent reduction upon addition

of 0. 1 ml heparin. Similar addition of 0.05 ml and 0.2 ml, respectively, of

heparin to 2 normal sera ( 1 .0 ml) resulted in a 1 3 percent decrease and 45

percent decrease in ionized calcium, respectively. Thus, it appears that observed differences in [Ca++] in sera and whole blood can be accounted

for by the heparin used as anticoagulant. Possible effects of erythrocytes on [Ca+^] have not been studied, however.

mM 2.0-

1.0-

0-1 1 1 1 1 1 0 200 400 600 800 1000

ADDED HEPARIN

(units)

Figure 14. Effect of heparin on ionized calcium concentration in aqueous solution. To

1.0 ml of standard solution containing S.OmM CaCl^and 150mM NaCl was added 0.02 ml increments of a commercial sodium heparin solution containing 10,000 units/ml. Data were obtained with static-type calcium electrode.
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 241

Heparin is a sulfated polysaccharide; although its ability to complex

calcium has long been suspected, these data appear to be the first actual

demonstration of such a complex. No formation constant can be given

since the molecular weight of heparin is unknown.

H. Accuracy of Electrode Measurements

As with any laboratory method, an important aspect of electrode analysis is the accuracy of the method, both in relative and absolute terms. An

estimate of the relative accuracy of both electrode (ionized) calcium and

EDTA (total) calcium measurements was obtained by analysis of vari- ance for duplicate measurements and expressed as the 95 percent confidence limit for the "true" value in any given sample. As may be seen in Table 4, variability of ionized calcium measurements with the static elec- trode was somewhat greater in serum than in ultrafiltrates. Replicate

variability with the flow-through electrode was one-third that of the static electrode and was comparable to that for total calcium by the EDTA

method. For a single value of 1 . 1 6mM in serum with the flow-through

electrode, the 95 percent confidence limit for the "true" value in that sample (±2 SD) would be between 1 . 1 3 and 1 . 1 9mM.

Table 4. Variability of replicate calcium determinations.

Ionized calcium mM

(Electrode)

Serum Ultrafiltrate Static Flow-through Static

electrode [47] [17] electrode [ 16] Mean

2 SD

1.14 0.09

1.16

0.03

1.17 0.07

Total calcium mM

(EDTA)

Serum Ultrafiltrate

[83] [16]

2.50 1.52

0.03 0.06

The present studies indicate that ionized calcium may be readily and

rapidly determined in serum, whole blood and ultrafiltrates with a high

degree of reproducibility. Relative accuracy therefore appears to be quite

satisfactory, as judged by low duplicate variability, reproducible [Ca+ +

] curves as a function of pH, high specificity for calcium ion, lack of

response to anions and chelates of calcium, quantitative recovery studies,

usefulness as end-point detectors in chelating titrations, and low variabili- ty within a given individual over extended periods of time. There is no

doubt that the electrodes respond to calcium ion in biologic fluids. Absolute accuracy is much more difficult to assess, for there is no ab- solute appeal or independent method of direct corroboration. There ap- pear to be 3 major considerations in this regard: 1) electrode response to
242 ION-SELECTIVE ELECTRODES

Other ions or non-ionic constituents of plasma, 2) variation in calcium ion

activity coefficients in biologic fluids as compared with calibrating stan- dards, and 3) variation in residual liquid junction potentials.

The first of these, i.e., response to other ions, would not appear to be of

great importance in most biologic fluids because of the very high specificity for calcium ion over Na+, K+, and Mg++. Absolute error resulting from

these ions is probably well below 5 percent.

It is possible that errors in apparent Ca++ could be produced by uptake

of plasma or ultrafiltrate constituents by the liquid ion-exchanger. While

such a possibility cannot be completely excluded, there are at least 3 findings which strongly argue against it: 1) observed electrode [Ca++]

values were within 5-10 percent of those reported for other methods, 2)

[Ca+^] values were very reproducible within a given individual overextended periods of time, presumably when other plasma constituents were

variable, and 3) the EDTA data in Figure 7 argue strongly against a

potential of non-calcium origin; upon addition of EDTA to serum or

ultrafiltrate, [Ca++] fell to a very low level. This would not be expected

if there were a significant non-Ca++ potential present.

Differences between calcium ion activity coefficients in biologic fluids as compared with calibrating standards are quite possible, but again are probably of no great significance. Although there is no experimental means by which individual ion activity coefficients can be determined,

Garrels [52] has found close agreement between yca++ values from

electrode measurements and those from Debye-Huckel theory up to total ionic strength 0.3 M. Since ionic activity coefficients are primarily related

to total ionic strength, the use of calibrating standards with total ionic

strength similar to that of plasma (i.e., ^ 0.16M) should minimize yca++

differences. Nevertheless, serum proteins may have effects on water

activity and apparent activity coefficients. Variation in residual liquid junction potentials (£)), particularly in protein-containing solutions, must always be considered in electrode measurements using a reference (calomel) electrode with liquid junction. As

noted by Bates [53], such potentials will generally be small when ionic

strengths of unknown and standard are similar. There is some evidence

which suggests that variation in Ej was not very great under the conditions of the present study. Thus, ultrafiltrate s are essentially simple salt solutions and little difference in junction potentials, as compared with

standard CaCl2-NaCl solutions, would be expected. That [Ca++] values were identical in serum and ultrafiltrates, as predicted from the generally

accepted monoligand dissociation of calcium-proteinate, suggests that junction potentials in sera and ultrafiltrates were not greatly different. Also, we have shown previously that Na^ activity in serum, as deter- mined with sodium-selective glass electrodes, is almost identical to that of pure NaCl solutions at corresponding concentrations after correction
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 243

for serum water content [54]. Nevertheless, it should be noted that with an electrode slope of 30 mV, a variation in liquid junction potential of

0.5 mV could produce an error of about 4 percent in apparent ionized

calcium concentration.

It is of interest to compare electrode [Ca+ +

] values with those obtained

previously by other methods. At least 3 methods have been used in the

past to estimate ionized calcium: 1) the frog heart method [3-5], 2) rachitic cartilage bioassay [55], and 3) metal ion indicators

[18-21,36,50,56] . Each of these has yielded average [Ca++] values of

about l.l-1.4mM in normal serum, which is rather close to the present mean electrode value of 1 . 1 4mM.

IV. Studies of Calcium-Binding by Normal Serum Proteins

We turn now to in vitro studies of protein-binding of calcium in normal

serum. Eight studies were made in 6 pooled normal serum samples

at room temperature (25±2°C), pH (7.3-7.4) and ionic strength

(0. 1 5-0. 16M). In two studies, pooled serum was serially diluted with

NaCl and in six studies CaCL-NaCl was serially added at constant total ionic strength. Ultrafiltrates of each serial sample were obtained as described above, with measurement of both total calcium [Ca] (EDTA

method) and ionized calcium [Ca++] (flow-through electrode) concentrations in each serum and ultrafiltrate. Serum proteins were also measured

as before in the six calcium-addition studies and in one of the two

serum-dilution studies. A. [CaProt] Vs. [Ca]

Resulting levels of protein-bound calcium [CaProt] are shown in Figure 1 5. Upon addition of calcium there was, as expected, a progressive

and slightly curvilinear increase in protein-bound calcium, rising to about

2.7mM at a total calcium level of S.OmM. Similarly, upon dilution with

NaCl, [CaProt] decreased progressively, falling to zero concentration at a total calcium level of about ImM. This intercept, rather than the ex- pected intercept of zero, may reflect experimental error; since serum

proteins, as well as calcium, were diluted to about 40 percent of their

original level, resulting [CaProt] levels were probably too low {i.e.,

10-20 percent of original values) to accurately measure by ultrafiltration.

B. Calcium Fractions OF Serum

Figure 1 6 shows the changes in each of the calcium fractions of normal serum upon dilution, or upon addition of calcium to serum. [CaR] levels were calculated as before, i.e., as the difference in ultrafiltrate [Ca] and

ultrafiltrate [Ca+ +

].
244 ION-SELECTIVE ELECTRODES

POOLED NORMAL SERA

[Co] mM

Figure 15. Observed calcium-proteinate concentrations as a function of total calcium in pooled normal sera upon dilution with NaCl or addition of CaCl2-NaCl at pH 7.3-7.4, 25°C and I =0.16M.

If it is assumed that electrode measurements in ultrafiltrates were accurate, i.e., in simple protein-free salt solutions, these data then allow an

evaluation of the accuracy of electrode measurements in serum. ''Calcu- lated" or expected ionized calcium concentrations in serum are indicated

in the figure.

C. Predicted Vs. Observed Serum [Ca++]

A comparison of the predicted [Ca++] values in Figure 16 and those

actually observed in serum with the electrode is shown in Figure 17. The

close correspondence between observed and predicted values provides

rather strong evidence that the electrode is not poisoned by protein in serum and suggests that residual liquid junction potentials and activity

coefficients may be quite similar in sera and ultrafiltrates. This is in ac- cord with the previous finding of virtually identical Ca++ values in sera and corresponding ultrafiltrates, as predicted by the generally accepted

monoligand dissociation of calcium proteinate.

D. Dissociation Constant of Calcium-Albuminate

In their frog heart studies, McLean and Hastings [3-5] showed that the

binding of calcium to serum proteins obeys the mass-law equation:
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 245

2.0 4.0 6.0 8.0

CCa] mM

Figure 16. Variation in the 3 calcium fractions of pooled normal sera upon dilution with NaCl or addition of CaCU-NaCl at pH 7.3-7.4, 25 °C, 1 =0.16/W. Methods for obtaining [CaProt] and [CaR] values are given in the text. Calculated [Ca++] values were obtained

as the difference in total calcium and the sum: [CaProt] + [CaR].

CaPror" Ca++ + Prot-(«+2) (6)

Valency in the above reaction is not critical and the equation for the

dissociation constant (A^caProt) may be written as: _ [Ca^^][Prot-]

/^CaProt [CaProt]

If we assume for the moment that calcium is quantitatively bound to albu- min, i.e., [CaProt] = [CaAlb] , this is simplified to: _ [Ca+ + ][Alb-]

/^CaAlb- [CaAlb]
246 ION-SELECTIVE ELECTRODES

POOLED NORMAL SERA

6.0 n

OBSERVED

[Co**]

mM

0-^- y . . . y . 1 1 1 2.0 4.0 6.0 8.0 [Ca] mM

Figure 17. Relation between predicted [Ca++] values, obtained from Figure 16, and those observed with the flow-through calcium electrode in pooled normal sera upon dilution with NaCl or addition of CaCl.-NaCl. (pH 7.3-7.4, 25 °C, I = 0. 1 6M.)

where [Alb-] is the total negative-site concentration available for calcium-binding and is equal to: [Alb-]=A7[Alb] - [CaAlb] (9) where [Alb] is the molar albumin concentration and n is the average max- imum number of negative sites available for calcium-binding per albumin

molecule. Substituting (9) in (8): [Ca^^](4Alb]- [CaAlb])

/^caAib- [CaAlb] ^ ^

We now have two unknowns: K' and n. As noted by Greenberg [9], if the range in observed [Ca++] values is sufficiently large, values for

(^caProt) and n may be obtained by rearrangement:

[Alb] _1 , K' 1 . [CaAlb] Ji n

' [Ca+^] ^

^ [Alb] _J

If the equation holds, a plot of [CaAlb] against [Ca++] should

yield a straight line with intercept of 1 and slope of K \ from which K'

is readily calculated. n n
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 247

Actually, the above equations are an oversimplification, since it is implicitly assumed that successive dissociation (negative) sites on the

protein molecule are identical and independent. From protein-binding

studies of Scatchard, Klotz and others [57-60], the assumption is probably not strictly correct. This, however, is beyond our scope here. Loken et al. [37], by ultracentrifugation, have observed that a plot of

[Prot]/[CaProtj against l/[Ca+ + ] is indeed linear in human serum at this pH. This, of course, does not necessarily mean that successive K'

values are identical, but suggests that differences are not detectable

at this pH and over the Ca++ range studied. The problem is further

complicated by the fact that serum proteins other than albumin also bind

calcium, presumably with different dissociation constants. Figure 18 shows our results upon addition of calcium to normal serum. For each point in the figure, it was assumed that the molecular weight of

albumin is 69,000 [61] and that 80 percent of the protein-bound calcium was bound to the albumin fraction. The reason for the latter figure will be

apparent in Section VIII below. The relationship appeared to be quite

linear, suggesting that the binding of calcium to serum proteins obeys the

mass-law equation, at least over the range in total calcium observed in man.From the intercept, a value of 8.4 negative sites per albumin molecule was obtained. This appears to be a very reasonable number. In his studies

with collodion membrane electrodes, Carr [14] obtained a value of 7-8

sites per molecule for fractionated bovine albumin.

The pK' for the reaction, derived from the slope of the function, was

2.18. This is in close agreement with previous studies [9] and is almost

the exact value obtained with the frog heart [4] and by ultracentrifugation

studies [37]. If it had been assumed that all protein-bound calcium was

bound to albumin, the value for n would have been 1 0.5 sites per molecule

but A^caAib would have been the same (pK' = 2.18).

From these data, we believe the calcium ion electrode provides a powerful new tool for the study of calcium-protein interaction. This will be illustrated further in Sections VII and VIII.

V. Distribution of Calcium Across the Blood-CSF Barrier

As an example of another type of physiologic problem, i.e., transport across biologic membranes, which can be readily studied with Ca++ elec- trodes, we will consider briefly the distribution of calcium across the

blood-cerebrospinal fluid (CSF) barrier. These studies were made in col- laboration with Dr. Andre Blum and have appeared in abstract form [62].
248 ION-SELECTIVE ELECTRODES

[Alb]

[CaAlb]

ASSUME: (CaAlb] = 80.0% [CaProt]

1.0-1

0.8-

0.6-

0.4-

0.2

0

y» 0.119 + 0.000780 X

( r ' 0.94 ) CoAlb « 6.55 X I0-' pK'« 2.18

0 200 400 600 800 1000 1200

I [Co**]

Figure 18. Dissociation constant of calcium-albuminate (K'caAib) upon addition of CaCUNaCl to pooled normal sera (6 studies) at 25 °C, pH 7.3-7.4 and I = 0.1 6M. Linearity of

the function suggests that the binding of calcium by human serum albumin obeys the mass-law equation for a mono-ligand association and that successive negative sites on

the protein molecule may be considered as identical and independent within limits of experimental error. For each point, it was assumed that 80 percent of the protein-bound calcium was bound to the albumin fraction. This figure was obtained from data pre- sented in Section VIII.

A. Previous Concepts

Table 5, excerpted from a current leading textbook of physiology [63]

,

summarizes previous data for the distribution of certain ions between

plasma and CSF. The "predicted" CSF/plasma concentration ratios for each ion are those expected if the ion were passively-distributed {i.e., by

simple diffusion), calculated by the Nernst equation for a 5 mV potential

difference (CSF +) between plasma and CSF. The latter value has been

observed experimentally in dog and goat by Held et al. [64] at normal serum pH.

The previously observed [Ch] distribution ratio of 1.21 is almost exactly that predicted for a passive process. In contrast, neither Na+ nor K+

appear to be in electrochemical equilibrium. The observed CSF/plasma
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 249

Table 5. Distribution of certain ions between cerebrospinal

fluid (CSF) and plasma.^'^

Ion CFS/plasma ratio

for passive distribution

Observed

CSF/plasma

ratio cr 1.20 1.21 Na+ 0.82 1.08 0.82 0.60

Ca^+ 0.68 0.50

^Predicted CSF/plasma concentration ratios are those for a

potential difference of 5 mV (CSF+), based on data of Held

et al. [64] ^ Observed ratios are those from the literature [63] ; Ca^^

refers to total, rather than ionized calcium, however.

[Na+] ratio (1.08) is higher than that predicted for a passive distribution,

suggesting an "active" or "facilitated" transport into CSF, while for K+

the reverse is true, suggesting active or facilitated transport out of CSF.

For Ca++, the observed ratio of 0.50 is lower than that predicted for a passive distribution (0.68), suggesting that Ca++ is also actively transported

from CSF to blood. This, however, refers to the distribution of total calc- ium and not Ca++ specifically. Since less than half of serum calcium is represented by Ca++, it seemed to us that such a conclusion is not necessarily justified. The following studies were therefore performed.

B. Ca++ Electrode Studies in Man and Dog

Spinal fluid was obtained by lumbar puncture from 5 hospitalized patients without evidence of central nervous system disease, and by cister- nal puncture in 5 healthy mongrel dogs. Venous blood was obtained

simultaneously and serum separated under oil as described above. Total

calcium (EDTA method), [Na], [K], [CI] and pH were measured in each serum and CSF sample, while [Ca++] was determined with the

flow-through electrode.

Results are summarized in Figure 19. Our observed CSF/plasma concentration ratios were in very close agreement with previous studies. The

observed ratio for total calcium (not shown) was 0.52 ± 0.01 (SE) in both
250 ION-SELECTIVE ELECTRODES

CHLORIDE

CI

1.4

1.2

.0- MAN DOG

0.9 n

0.7

05

(N.S.) (N.S.) POTASSIUM

MAN DOG

SODIUM

1.2-1

Na

1.0-

0.8 MAN DOG

p< 0.001 p<O.OOI IONIZED

CALCIUM

I.O-i

0.8-

06-

MAN DOG

p<0.05 p-cO.OS p<O.OI p<O.OI

Figure 19. Observed CSF/serum distribution ratios in man (lumbar fluid) and dog (cister- nal fluid). Dashed lines for each ion represent theoretical passive-distribution ratios for a 5 mV potential difference between CSF and blood. Note that Ca++ ratios, determined

with the flow-through electrode, were higher than that predicted for a passive-distribution

in both man and dog. man and dog, almost exactly that noted previously (Table 5). In contrast,

the distribution of Ca++, determined with the electrode, was significantly

higher in both man and dog than that predicted for a passive distribution: 0,73 ± 0.01 (man) and 0,83 ± 0,02 (dog). The latter value in the dog was

significantly (p < 0.01) higher than that in man. While this may represent some species differences, it seems likely related to the more proximal

(cisternal) sampling site in dogs than in man (lumbar). Thus, after its entry

into CSF from the choroid plexus, [Ca++] may decrease progressively

down the spinal canal by back-diffusion into blood.

We conclude from these studies that [Ca++] in CSF is not in elec- trochemical equilibrium with plasma. In contrast to observed total calci- um ratios, observed calcium ion ratios suggest that Ca++ is transported

from blood to CSF (presumably by an active or facilitated process) and

not from CSF to blood, as held previously.
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 251

VI. Studies of Hyperparathyroidism

Turning now to an entirely different problem, we [65] have recently

had the opportunity of studying a 34 year old white female with hyperparathyroidism and hereditary neurofibromatosis:

In June 1967, the patient noted numbness of the lips and face and was

later admitted to a psychiatric hospital where a diagnosis of schizophrenia was made and a lump in the left neck noted. In early 1 968, serum total cal- cium was repeatedly elevated. She was admitted to our Metabolic

Research Unit in September 1968; her subsequent course is summarized

in Figure 20. HYPERPARA THYROIDISM

( R.K. 34 W 9 ) mM PARATHYROID

0.8-^—I—r—1—I—I—r—1—r^S—1

r>H—r"- 1 1 1 T—"—r'

16 22 26 30 14 18 30 4 5 6 7 6 12 Sept. Oct. Nov HPS. POST-OP 0 12 24 48 72 96

Figure 20. Serum total and ionized calcium values in a patient with primary hyperparathyroidism. Note that total calcium values fell preoperatively to within the normal range, while ionized calcium values remained consistently elevated. On admission, serum total calcium was 3.0mA/ (12 mg%) about 1 S.D.

above our 95% normal confidence limit, indicated by the upper band in Figure 20. Serum ionized calcium was 1.6mM, some 4 S.D. above the

upper normal limit, indicated by the lower band. Serum parathormone

level, kindly determined by Dr. Armen Tashjian, was also elevated, as measured by radioimmunoassay [66].

In the following weeks, her serum total calcium slowly declined to within the normal range, in association with a reduction in serum albumin

level. Serum ionized calcium, however, determined with the electrode,

remained elevated. If she had been first seen at this time and only total calcium measured, the diagnosis of hyperparathyroidism might have

been overlooked.

348-381 0-69— 18
252 ION-SELECTIVE ELECTRODES

In an effort to stimulate the release of parathyroid hormone, an in- travenous infusion of di-sodium EDTA was given in October 1968 and

[Ca++] monitored with the flow-through electrode at 5-10 min intervals,

using heparinized whole blood.

Results are shown in Figure 21. (To our knowledge, these data

represent the first measurements of Ca++ upon administration of EDTA

HYPERPARA THYROIDISM

95 %

NORMAL [Co**l CONFIDENCE INTERVAL

f i

.1.

1 .

1 t1 I

1 1 1 1 1 -30 0 +30 60 90

TIME (MINUTES)

Figure 2L Effect of intravenous infusion of di-sodium EDTA (ethylenediamine tetra- acetate) on serum total and ionized calcium concentrations in a patient with primary

hyperparathyroidism. Vertical scales are adjusted to show the parallel and nearly identical decrease in total and ionized calcium. [Ca] values were determined by EDTA titration; [Ca] measured by atomic absorption spectroscopy (not shown) remained constant throughout the infusion. in vivo.) The infusion consisted of 20-40 mg/kg/30 min of di-sodium

EDTA in isotonic NaCl administered into one arm while blood was obtained from an indwelling catheter in the other arm. Within minutes, a decrease in blood [Ca++] was observed; [Ca++] similarly rose within

minutes after stopping the infusion. The decrease in [Ca+^] was accompanied by an identical decrease in total calcium as determined by the

EDTA method (total calcium determined by atomic absorption spec- troscopy, not shown in Figure 2 1 , remained quite constant; the difference

between the two methods reflected calcium chelated by administered

EDTA).

On November 4. she underwent surgery and two large hyperplastic

parathyroid glands were removed. Both total and ionized calcium were
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 253

measured following induction of anesthesia and at intervals after removal

of the parathyroids (Fig. 20). Within an hour, both total and ionized calci- um had begun to fall. The change in ionized calcium was more abrupt,

decreasing about 30 percent within 3 hours. Serum total calcium

remained below normal for over a week. Ionized calcium was also below

normal for several days and during this time she had mild tetany.

It is evident from these studies that the calcium ion electrode may pro- vide an important new tool in clinical medicine, both in diagnosis and in evaluation of therapy.

VII. Studies of Serum Calcium in Cirrhosis [67]

In our studies of normal subjects (Section III, above) it was

emphasized that no correlation was observed between ionized calcium

and total calcium concentrations in normal serum. Increase in serum total calcium was almost quantitatively accounted for by an increase in protein-bound calcium; from this it was concluded that, in the normal, a serum total calcium measurement is an indirect measure of the serum al- bumin level. The basis for this statement will be developed more fully in the present section, in which another group of normal subjects is compared with patients with advanced cirrhosis of the liver. Patients with cirrhosis are of particular interest for several reasons: 1) they often have a reduction in serum total calcium, 2) they frequently

have reduced serum albumin levels (the major site of calcium-binding in normals), 3) with concomitant elevation of serum globulins, and 4) they

frequently have respiratory and/or metabolic alkalosis, yet clinical tetany

has not been recognized in over 1000 consecutive cirrhotic patients at the

Shattuck Hospital during the past 13 years. This suggests that, unlike serum total calcium, serum ionized calcium may be relatively normal in this disease. Cirrhotic patients are thus of particular interest for the study

of the binding of calcium to the serum proteins and the complex

physiologic and physicochemical factors governing the level of Ca++ in human serum.

Studies were made in 42 hospitalized patients with advanced cirrhosis,

25 males and 17 females whose age ranged from 33 to 82 years (mean:

50.4 years). All patients admitted to at least moderate alcohol intake and

the majority were considered to be chronic alcoholics. Diagnosis was

established by liver biopsy in 27 patients and by clinical and laboratory

findings in the remainder. Of the biopsied patients, 18 were considered to have "Laennec's cirrhosis", 4 "post-necrotic", and in 5 the cirrhosis was

of questionable type. Of the non-biopsied patients, all were considered to have cirrhosis of the alcoholic. Marked ascites was present in 24 patients;

1 1 others had mild ascites. The majority were clinically stable at the time

of study.
254 ION-SELECTIVE ELECTRODES

Studies were also made on 21 healthy volunteer hospital personnel, 6

males and 15 females whose ages ranged from 20 to 61 years (mean: 30.5

years). Eight of these subjects were included in the above studies of 60

normal subjects (Section III). Venous blood was obtained under oil without anticoagulant, usually 2-3 hours after breakfast. Following centrifugation under oil, an aliquot of serum was removed for pH measurement; the remaining serum was again

placed under oil without exposure to air. A heparinized blood sample was

obtained simultaneously for determination of whole blood pH. Most

[Ca++] measurements in the cirrhotic patients (32 of 42) were made

with static-type electrodes (Figs. 2, 3). In the normals, 8 subjects were

studied with static electrodes and 1 3 with flow-through electrodes (Fig.

4), as described above.

A. Calcium Fractions of Serum

As shown in Figure 22a, serum total calcium was significantly reduced

in the cirrhotic patients. Mean serum [Ca] in the 21 normal subjects was

2.47 ±0.08'^ mM as compared with 2.16±0.08mM in cirrhotics (p <

0.001). In contrast, total ultrafiltrate (diffusible) calcium was significantly

increased (p<0.01) in the latter group. Mean values in normals and

cirrhotics were 1.47±0.06mM and 1.62±0.6mM, respectively. Thus,

of the total serum calcium, a significantly (p< 0.001) higher fraction was diffusible in the cirrhotic patients: in the normal, an average of

59.8 ±2.8 percent was ultrafiltrable, while in the cirrhotics 75.5 ±3.6

percent of the serum total calcium was represented by the diffusible [Ca++ + CaR] fractions. These data indicate a significant reduction

in protein-bound calcium in the cirrhotics, as shown in Figure 22c.

Mean [CaProt] in normals was 1 .00 ± 0.09mA/, almost twice the

value of 0.54±0.09mM in cirrhotics (p< 0.001).

In the absence of electrode data for ionized calcium, the observed in- crease in total diffusible calcium might be interpreted as suggesting that [Ca+ +

] is normal or increased in such patients or, alternatively, that if [Ca+^] were decreased, the increase in ultrafiltrable calcium would

reflect an increase in diffusible complexes, [CaR].

That the latter is the case is shown in Figure 23. Serum ionized calcium was significantly reduced in the cirrhotic patients as compared with nor- mals, with means of 1 .09 ± 0.06mM and 1 . 1 6 ± 0.02mM, respectively (p

< 0.02). While these mean values were ''significantly" different, there was considerable variability in [Ca+ +

] in the cirrhotic group. As was the case with serum total calcium, about half of the cirrhotic patients were below the lowest value observed in the normals but, unlike total calcium,

5 of the 42 patients ( 1 2 percent) were above the highest normal value. These and all subsequent values refer to ± 2 SE of the mean.
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 255

(a) mM

3 0

2.5

2.0

1.5

1.0-

SERUM

TOTAL CALCIUM

NORMAL CIRRHOSIS

(21) (42)

2 471008 2 1610.08

p< 0.001

(b) mM

2.5

2.0-

1.5-

1.0-

0.5-

ULTRAFILTRATE TOTAL CALCIUM

i:

NORMAL CIRRHOSIS

(21) (42)

1.4710.06 1.6210.06 p< 0 0!

(c) mM

1.0

[CaProt]

0.5-

••

•••

• •.V

NORMAL CIRRHOSIS

(21) (42) 1.0010 09 0.5410.09

p< 0.001

Figure 22. (a) Observed total calcium concentrations [Ca] in sera from 2 1 normal subjects and 42 patients with cirrhosis, (b) Observed [Ca] concentrations in serum ultrafiltrates.

(c) Calculated concentrations of protein-bound calcium [CaProt]. In this and subsequent

figures, enclosed boxes represent mean values ±2 standard errors.

(a) SERUM

IONIZED CALCIUM

•••

•

•

•••

•t*

NORMAL CIRRHOSIS

(21) (42)

, 1.1610.02 1.0910.06

/ p<0.02

(b)

mM

1.4-

1.2-

1.0-

0.8-

0.6-

ULTRAFILTRATE

IONIZED CALCIUM

NORMAL CIRRHOSIS

(16) (41)

1.13 1 0.02 1.07 10.04

( p<0.05

(c)

mM

1.5-1

[CoR]

0.5-

NORMAL CIRRHOSIS

(21) (42) 0.3210.06 0 551 0 06

p<000l

Figure 23. (a) Observed serum ionized calcium concentrations in 21 normals and 42

cirrhotic patients, (b) Observed ultrafiltrate ionized calcium concentrations in 16 normals and 41 cirrhotics, (c) Calculated concentrations of diffusible calcium complexes [CaR]

in sera from 21 normals and 42 cirrhotics.

Ultrafiltrate [Ca^ '] was almost identical to that in serum for the two

groups. In each group the average difference between serum and ultrafil- trate [Ca+ +

] was 0.02- 0.03 mM.
256 ION-SELECTIVE ELECTRODES

As expected from the significant increase in total diffusible calcium and

decrease in serum [Ca++] in cirrhotic patients, the concentration of dif- fusible calcium complexes, [CaR], was significantly increased in the cir- rhotic group. Mean [CaR] was 0.55 ± 0.06mM, or 72 percent higher than

the mean of 0.32 ± 0.06mM in normals (p < 0.001).

From Figures 22 and 23, it is concluded that in cirrhosis there is a

significant: 1) decrease in serum [Ca] and [CaProt], 2) decrease in serum

[Ca++], 3) increase in [CaR], and 4) increase in total diffusible calcium.

The relative contributions, in percent, for each of the 3 calcium frac- tions for both normals and cirrhotics are shown on triangular coordinates

in Figure 24. Cirrhotic patients tended to fall in that area of the triangle

characterized by decreased [CaProt], increased [CaR] and normal or in- creased [Ca++].

[Ca*+] = l00 7o

[CaProt]

Figure 24. Relative contribution, in percent, of each of the 3 calcium fractions of serum

in 21 normals (closed circles) and 42 cirrhotics (open circles). Note that cirrhotics tended

to fall in an area characterized by decreased [CaProt], increased [CaR] and normal or

increased [Ca++]. In the normal group, [Ca++] constituted an average of 47.1 ± 1.7 per- cent of the serum total calcium, as compared with 50.9 ± 2.6 percent in cirrhotics. This difference was not significant. Thus, while [Ca++] was

significantly reduced in cirrhotics on an absolute scale, that fraction as [Ca++] was somewhat increased. In the normal, [CaProt] averaged

40.2 ± 2.8 percent of the total calcium, which was significantly (p <

0.001) greater than the value 24.4 ±3.6 percent in cirrhotics. [CaProt] was thus reduced on both absolute and percentage scales. [CaR]

averaged 12.7 ± 2.2 percent of the total in normals, as compared with 24.6
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 257

± 2.4 percent in cirrhotics (p < 0.001). [CaR] was thus increased in both

relative and absolute terms.

B. Serum Proteins

Total protein, albumin and globulin levels in serum are given in Figure

25. In the normal group, mean total protein was 72.3 ± 2.2 g/1, which was

significantly greater than the value 64.4 ±3.3 g/1 in cirrhotics (p < 0.01). In the latter, total protein was quite variable, ranging from 35 to 90 g/1. The reduction in total protein in the cirrhotics was due to marked

reduction in serum albumin concentration. Mean [Alb] in normals was

47.3 ± 2.2 g/1 as compared with 29.3 ± 2.5 g/1 in cirrhotics (p < 0.001).

Serum [Glob] was significantly increased in the cirrhotic patients, with

a mean of 35.6 ± 2.6 g/1 as compared with 25.0 ± 2.0 g/1 in normals (p <

0.001). There was no correlation in the cirrhotics (r= —0.16) and only a

slight correlation in normals (r = —0.46) between serum [Alb] and

[Glob].

(a) (b) (c) SERUM TOTAL PROTEINS

qm/l90-

70-

60

40-

:

NORMAL CIRRHOSIS

(21) (41) 723122 644*3.3

( p<0,Ol )

SERUM ALBUMIN

gm/l qm/l 60-

•«•• 60-

50- •• ^ : 50-

40-

<. A,

40-

30- 30-

20- ST

•••

•

• 20-

10-

• 10-

0- NORMAL CIRRHOSIS

(21) (41) 473* 2.2 293* 2.5

( p< 0.001 )

0-

SERUM GLOBULINS

4h

NORMAL CIRRHOSIS

(21) (41) 25.0*2.0 35 6* 2.6

( p< 0.001

)

Figure 25. Serum total protein (a), albumin (b), and globulin (c) concentrations in 21 normal subjects and 41 patients with cirrhosis.

C. Relation of [Ca+ + ] to Total Calcium and Albumin

As shown in Figure 26a, there was no correlation between serum

ionized calcium and serum total calcium in either normals or cirrhotics. Serum [Ca++] was within a rather narrow range regardless of the total calcium level. Thus, measurement of total calcium did not provide an ac- curate index of serum ionized calcium in these patients, an observation
258 ION-SELECTIVE ELECTRODES

similar to that noted (Section III) in normal subjects. As noted above, the

95 percent confidence limit for ionized calcium in the normal was

1.01-1.26mM, indicated by the shaded area in Figure 26. Thus, in the 42

cirrhotics, there were 14 patients (33%) outside the 95 percent normal

confidence limit, 4 with elevated [Ca++] levels and 10 with reduced

[Ca"^] values. As may be seen in Figure 26b. there was also no correlation between serum [Ca^-] and albumin levels in either normals or

cirrhotics.

SERUM

[Ca^]

(mM)

SERUM

[Ca^^]

(mM)

1.4

1.2

1.0

0.8-

L

195 %

NORMAL

CONFIDENCE

INTERVAL

• = NORAAAL

o= CIRRHOSIS

T 1 1 1 1

1 I .6 1.8 2j0 2.2 2.4 2j6 2.8 SERUM TOTAL CALCIUM

(mM)

0.8-

195 %

NORMAL

CONFIDENCE

INTERVAL

• = NORMAL

o = CIRRHOSIS

" 1 1 1

1 I 10 20 30 40 50 60

SERUM ALBUMIN

(gm/l)

Figure 26. (a) Relationship between serum ionized calcium and serum total calcium concentrations in 21 normals (closed circles) and 42 cirrhotics (open circles), (b) Relationship between serum ionized calcium and serum albumin concentrations in 21 normals

(closed circles) and 41 cirrhotics (open circles). The shaded areas represent the 95 per- cent confidence interval for serum [Ca ] in normal subjects (Section III). Note the complete lack of correlation; ionized calcium was within a rather narrow range, irrespective of total calcium and albumin concentrations.
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 259

D. Relation of [CaProt] to Serum Proteins

It is concluded from these data that, although [Ca++] is significantly

reduced and [CaR] significantly increased in cirrhotic patients, the

overall reduction in serum total calcium is primarily due to marked reduction in protein-bound calcium, [CaProt]. Since albumin has long been

recognized as the primary site of calcium-binding in serum, reduced

[CaProt] might be expected to accompany significant reduction in serum albumin.

The relation between [CaProt] and [Alb] levels for both normals and

cirrhotics is shown in Figure 27. Individual subject data are given in Figure 27a, while in Figure 27b, samples were pooled by 5 g/1 increments

in serum albumin. [CaProt] was linearly related to serum albumin con- centration in both normals and cirrhotics. There are two questions: 1) is calcium bound entirely to albumin, or is there also some binding to serum globulins and 2) does a biochemically

diseased liver produce qualitatively abnormal albumin {i.e., in terms of

calcium-binding affinity) or is reduction in [CaProt] purely quantitatively

related to reduction in [Alb]?

The first question relates primarily to the intercept(s) of the function(s)

in Figure 27, while the second is primarily related to the slope(s) of the

function(s). Both, of course, are mathematically and physicochemically

interrelated. The linear relationship between [CaProt] and [Alb] indicates that most (perhaps all) of protein-bound calcium is bound to albumin. (There was no relationship between [CaProt] and serum globulin levels in either

normals or cirrhotics]. That calcium is bound entirely to albumin in cirrhotics is suggested by the intercept on the horizontal axis in Figure 27b. If there were measurable binding to globulins, an intercept on the vertical axis would be expected, particularly in view of the

significant elevation of serum globulins in these patients. Since, from the

mass-law equation an intercept on the horizontal axis would make no

physicochemical sense, it is likely that the true intercept of the function

is zero in cirrhotics, in which case calcium may be considered to be

quantitatively bound to albumin in these patients.^

it would appear that there were no detectable qualitative differences

between normals and cirrhotics since, as shown in Figure 27b, the slopes

of the calculated regressions for the two groups were almost identical,

0.0190mM/g and 0,0197mM/g respectively. If the molecular weight of

albumin is 69,000 in both groups, this would correspond to 1.31

^ The intercept on the horizontal axis may reflect the fact that ultrafiltrates were obtained

at 25 °C rather than 37 °C. As noted in Section III.B., data of Loken cf ^//.[37] indicate that [CaProt] is about 5-6% higher at 37 °C than at 25 °C.
260 ION-SELECTIVE ELECTRODES

(a)

1.5 • • = Normal

o = Cirrhosis

[CaProt]

(mM)

1.0-

0.5-

•

9> o*« •

'8P 8<> o

rso ^ ft o o o 8 O o

—I 1 1 1

10 20 30 40

SERUM ALBUMIN

(gm/l )

50 —

I

60

SERUM ALBUMIN

(gm/l ) Figure 27. Relationship between protein-bound calcium [CaProt] and serum albumin

concentrations in 21 normals and 41 cirrhotics. Individual subject data are given in (a). In (b), data from normals and cirrhotics were each pooled by 5 g/1 increments in serum

albumin. Vertical bars represent ±2 SE. Note that the slopes of the calculated least- squares regressions in (b) were almost identical in the 2 groups. In normals, the cal- culated intercept was 0.1 1 mM while in cirrhotics, it was very nearly zero.

molecules of calcium per molecule of albumin in normals, and 1.36 in cirrhotics. In normals (Fig. 27b), the calculated intercept of 0.1 ImM on the verti- cal axis suggests some binding to serum globulins. Since mean [CaProt]

in the normal was 1 .OmM (Fig. 22), the data suggest that about 1 1 percent

of protein-bound calcium is in the globulin fraction. The extrapolation is quite long, however, and as will be shown in Section VIII, this problem

is perhaps better studied by another type of mathematical analysis.
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 261

Mean /CcaAib values, calculated by Equation (10), were 7.43 ±0.64

(xiO-3), {pK' = 2A3) in the normals and 10.06±2.74 (x 10-^),

(pK' = 2.00) in cirrhotics. While K' values in the majority of cirrhotics were within the normal range, some 15-25 percent of patients showed

values 2-6 times those of normals. This suggests that the calcium-binding

affinity of serum albumin may be decreased in some patients. These data

should be viewed with extreme caution, however, owing to the uncertainties in K' calculations (Section IV.D.) and to variation in other

factors, such as pH and complexing anions, which may affect calcium

binding.

E. Relation of Total Calcium to [CaProt] and [Alb]

As noted above, [CaProt] decreased linearly with decreasing albumin

concentration. Although [Ca++] was significantly decreased and [CaR]

significantly increased in the cirrhotics, the resulting relationship between serum total calcium and [Alb] was also linear, as shown in Figure 28. Both normals and cirrhotics appeared to fall on the same regression. If the

extrapolation is valid, the data suggest that at zero albumin concentration, serum [Ca] would be 1.61mM.

The slope of the function in Figure 28b (0.019mM/g) is identical to those in Figure 27b, indicating that reduction in serum [Ca] paralleled the

reduction in [CaProt]. That this is the case is shown in Figure 29. The

slope, 0.92 in both normals and cirrhotics, indicates that reduced

[CaProt] accounted almost quantitatively for the reduction in serum

total calcium. The extrapolated value for [Ca] at zero [CaProt] was 1.57mM in cirrhotics and 1.33mM in normals. (The displacement of the

intercept on the horizontal axis in the cirrhotics reflected the increased

[CaR] fraction in these patients.) F. pH Effects: Nomograms for [CaProt]

.

We will now consider the effect of pH on serum ionized calcium and

protein-bound calcium. Nomograms will then be constructed for

[CaProt] in both normals and cirrhotics for any given pH and albumin

level. In our static electrode studies of normal serum (Fig. 12, Section III.C),

it was noted that [Ca++] decreased progressively and nearly linearly with

increasing pH. The effect was accentuated upon concentration of the serum proteins. In the 52 normals so studied, the following data were obtained:

[Ca]j: =2.505mM

[Ca++]j - 1.36mMatpH 6.8 [Ca+ + ]5 =0.94mMatpH 7.8
262 ION-SELECTIVE ELECTRODES

(a)

3.0

SERUM

TOTAL

CALCIUM

(mM)

2.0-

1.0-

Y» 1.65 +0.018 X

( r 0.74 ) • NORMAL

o CIRRHOSIS —I

20 —I40 —

I

60

SERUM ALBUMIN

(gm/i)

(b)

3.0 n POOLED DATA

SERUM

TOTAL

CALCIUM

(mM)

2.0-

1.0-

Y-I.6I + 0.0I9X

( r 0.94 ) —I

40 —

I

20 60

SERUM ALBUMIN

(gm/l)

Figure 28. Relationship between serum total calcium and serum albumin concentrations

in 21 normals and 41 cirrhotics. In (b), the data were pooled by 5 g/1 increments in serum

albumin. Vertical bars represent ±2 SE. Note that both normals and cirrhotics appeared

to fall on the same regression and that the slope of the function was very nearly identical

to those in Figure 27b.
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 263

(o)

1.5 • > Normal OS Cirrhosis

1.0 [CaProt] (mM)

Y»-l.68+ I.05X

( r«0.8l) 0.5-

0-H —I

0.5 1.0 4s 8i 2j0 —I

2.5 SERUM TOTAL CALCIUM (mM)

3.0

(b) POOLED DATA

[CaProt]

(mM)

0.5-

SERUM TOTAL CALCIUM

( mM ) Figure 29. Relationship between protein-bound calcium [CaProt] and serum total calcium

concentrations in 21 normals and 42 cirrhotics. In (b), data were pooled by 5 g/l in- crements in serum albumin. Vertical bars represent ±2 SE. Note that the slopes were

identical in the 2 groups; the observed slope of 0.92 indicates that the change in serum

total calcium was almost quantitatively accounted for by the change in the proteinbound fraction. The displacement of the curve to the right in cirrhotics reflected the increased [CaR] levels in these patients. Predicted [Ca] levels at zero [CaProt] concentration were 1.33 and \.51mM in normals and cirrhotics, respectively.

Thus, at pH 6.8, an average of 54.3 percent (1.36/2.505) of the serum

total calcium was ionized, while at pH 7.8 it was 37.5 percent. In other

words, a 1 unit pH change resulted in a 16.8 percent (54.3-37.5) decrease

in the ionized calcium fraction of normal serum. This is virtually identical

to the change in free calcium of normal serum noted by Loken et al. [37]

,

as determined by ultracentrifugation. From this, we may surmise that a pH-induced decrease in ionized calcium is accompanied by a correspond-
264 ION-SELECTIVE ELECTRODES

ing increase in protein-bound calcium. (As noted in Section III.E. above,

the common diffusible complexes of calcium in serum do not appear to be

pH-dependent in this pH range.)

Stated another way, the average change in serum [Ca++] for a 1 unit

pH change was 0.42mM. If we may apply this figure to the present group

of 21 normal subjects in whom the serum proteins were also measured,

the value 0.42mM thus represents that change in [CaProt] produced at an average serum albumin concentration of 47.3 g/1 (Fig. 25) and average

globulin concentration of 25.0 g/1 (Fig. 25). The change in [Ca++] or [CaProt] would be expected to be proportionately greater at higher

protein concentrations (Fig. 1 2) and proportionately less at lower protein

concentrations. In other words, the absolute change in [CaProt] induced by

pH change would be expected to be proportional to existing protein levels, while the percentage change in [CaProt] would be expected to be constant. In the present series of 21 normal subjects, average [CaProt] was l.OOmM (Fig. 22) and average serum pH at the time of ultrafiltration was 7.42 ± 0.01 (2 SE). The following equation may therefore be written

relating [CaProt] to [Albumin], [Globulin] and pH:

[CaProt] =[CaAlb]- [(0.42)^^ (7.42 -pH)]

+ [CaGlob]- [(0.42) (7.42- pH)] (12)

where pH is that at the time of ultrafiltration. We now need a way of estimating [CaAlb] , i.e., calcium bound to albu- min, and [CaGlob], calcium bound to globulins. This can be obtained

from the slope of the function in Figure 27: [CaAlb] =0.0190 [Alb] (13)

Since the average [Alb] in the 21 subjects was 47.3 g/1: [CaAlb] = (0.019) (47.3) =0.899mM (13a)

Since average [CaProt] was l.OOmM, the remainder (0.101mA/)

represents [CaGlob], at an average [Glob] level of 25.0 g/1. Thus:

[CaGlob] = 0. 101 = (z)(25.0) (14)

where z = 0.004mM/g. Equation (12) may thus be re- written in terms of

known quantities:

[CaProt] =0.019[Alb]- [(0.42) ("^y) (7.42-pH)]

+ 0.004[Glob]-[(0.42) (-^^^) (7.42- pH)] (15)
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 265

The correspondence between observed [CaProt] levels, determined by

ultrafiltration, and those calculated by Equation (15) was rather close. Thus, in the 21 subjects, average calculated [CaProt] was l.OOmM, exactly that observed experimentally, while the average error (without re- gard to sign) was 0.135 ±0.02 (SE)mM or 13.5 percent.

The constants 0.019 and 0.004 in Equation (15), i.e., albumin and

globulin binding constants, will be derived in a different manner in Section

VIII below, and will be found to be 0.0167 and 0.0079, respectively. The

use of these latter constants in Equation (15) yielded almost identical

results, however. Thus, mean calculated [CaProt] was 0.99mM and

average error was 0.131 mM or 1 3 . 1 percent.

Our best estimate of [CaProt] from measured albumin, globulin and

pH thus appears to yield an average error of about 13 percent in normals.

While this is close enough for most clinical purposes. Equation (15) does

not readily lend itself to a bedside solution. Clearly, a simple nomogram

is desirable, but this is not easily done with 3 measured variables and a constant fractional amplification. A simple solution was obtained as follows:

If we assume that all protein-bound calcium is bound to albumin, then

from observed mean values of: [Alb]j = 47.3 g/1 (16)

[CaProt] ^= 1.00 mM= [CaAlb]^- (17)

Neglecting the pH term: [CaAlb] = 0.0211 [Alb] (18)

and with the pH term: [CaAlb]=0.0211[Alb]-[(0.42) (i^) (7.42-pH)]

^^^^ Equation (19), with only two measured variables, is readily expressed

graphically as a nomogram. This is given in Figure 30. Using this nomogram, average calculated [CaProt] in the 21 subjects was l.OOmM, exactly that observed experimentally and the average error was 0. 136mM

or 13.6 percent. The reason for the close correspondence of values calculated by Equations (12), (15) and (19) is of course the small variations in albumin, globulin and pH. In fact, we would have done as well if the pH

term in Equation (19) had been neglected altogether. Neglecting the pH

term, mean [CaProt] was l.OOmM and the average error was 13.5 percent. pH is therefore included in the nomogram more for the sake of

emphasis than for the sake of accuracy.

In cirrhosis the situation is already simplified since, from Figure 27,

there was no detectable binding to globulins and there would therefore be
266 ION-SELECTIVE ELECTRODES

^ 8 S ? » S S
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 267

no globulin term in the equations. The faulty intercept on the horizontal

axis in cirrhotics has already been noted, probably relating to a temperature effect as well as to analytical and regression analysis errors. The observed slope in cirrhotics, 0.0197 yielded calculated [CaProt] values

about 15 percent too high. From observed mean [Alb] and [CaProt],

values of 29.3 g/1 and 0.54mM respectively, the correct slope may be esti- mated to be: 0 54 ^=0.0184 mM/g

and estimated [CaProt] from existing albumin and pH levels would be: /[Alb]\

[CaProt] = 0.0184 [Alb] -[ (0.42) ^——^ (7.42 - pH)] (20)

\ 47. o / The resulting nomogram is given in Figure 30. Mean calculated [CaProt] in the cirrhotics was 0.54mM, exactly that observed experimentally, and the average error was 0.193 ± 0.02mM.

Since mean [CaProt] was only about half that in normal subjects, the

overall percentage error was much larger than in normals, 35.7 percent.

While this may largely reflect analytical errors at low albumin and

[CaProt] concentrations, it is possible that other variables affecting

protein-binding of calcium should also be considered. In particular, one wonders about the elevated [CaR] levels in these patients; we do not yet

know what these complexing anion(s) are, although it would not appear to be phosphate.

As in normals, the accuracy of estimated [CaProt] levels in cirrhotics

[Eq. (20)] was not improved by the pH term. In fact, the error was somewhat less without it. Thus, neglecting the pH term, average

[CaProt] was 0.54mM and the average error was 0. 188mM or 34.8 percent. The reason for this rather surprising result is undoubtedly related,

in part at least, to the fact that those patients with large deviations in blood pH also tended to have the lowest albumin levels, i.e., these were

the most severely ill patients. Since the absolute change in [CaProt] in- duced by pH change is related to the albumin level, the overall pH effect was quite small. For example, the lowest blood pH observed was 7.09,

obtained a few minutes before demise, while [Alb] was also the lowest

observed, 12 g/1. Observed [CaProt], determined by ultrafiltration, was

0.1 8mM, while that calculated by Equation (20) was 0.188mM. Without

the pH term, calculated [CaProt] was 0.22mM, or only 0.04mM error. Thus, while pH must be considered an important theoretical factor in these patients, the overall effect is quite small and, as in normals, is in- cluded in the nomogram more for the sake of emphasis than for the sake

of accuracy.

348-381 0-69— 19
268 ION-SELECTIVE ELECTRODES

Finally, it should be noted that the nomograms were constructed for data obtained at 25 °C. From data of Loken 6^ al. [37], corresponding

values in vivo would be about 5 percent higher.

G. Summary

The data from cirrhotics are summarized in Figure 3 1 , in which serum

total calcium and each of the 3 calcium fractions are given as a function of serum albumin concentration. Note that mean serum [Ca++] remained

unchanged with decreasing albumin concentration. [CaR] was significantly elevated above normal and increased slightly with decreasing albu- min concentration.

3.0

1

SERUM

TOTAL

CALCIUM

(mM)

SERUM ALBUMIN

(gm/l

)

Figure 3 1 . Summary figure for the relationship of serum total calcium concentration (upper

line) and each of the 3 calcium fractions of serum (shaded areas) to serum albumin concentration (Fig. 26). Decrease in serum total calcium was virtually quantitatively ac- counted for by decrease in protein-bound calcium. At zero albumin concentration, the extrapolated value for serum total calcium was 1.61mM (Fig. 28).

In cirrhotics, as well as in normals, change in serum total calcium was

almost quantitatively accounted for by a corresponding change in protein-bound calcium. The latter, in turn, reflected the serum albumin

level. In contrast to normals, there was no detectable binding to serum

globulins in the cirrhotics.
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 269

While cirrhotics are a heterogeneous population, with several variables

affecting serum calcium, the overriding consideration is the serum albu- min level, as shown in this model.

VIII. Studies of the Hypercalcemia of Cancer^

In both normals and patients with cirrhosis, it was emphasized that serum ionized calcium concentrations were within a rather narrow range, independent of serum total calcium and albumin concentrations. In both

groups, variation in serum total calcium was almost totally accounted for by variation in protein-bound calcium, mainly to serum albumin.

Hypercalcemia is a common and often distressing complication in patients with certain types of malignancy. As a final example of the useful- ness of calcium electrodes in biomedical research and clinical medicine,

we will now consider some results of 30 studies recently performed in 24

patients with cancer and hypercalcemia. Comparison will be made with

the 21 normal subjects presented in Section VII. It will be shown that,

although serum protein abnormalities are comparable to those in cirrhosis, there are striking differences in serum ionized calcium and in the

protein-binding of calcium in these patients. As was given for cirrhotics, a model will be developed for total calcium and each of the 3 calcium frac- tions of serum in normals and in the hypercalcemia of malignancy.

A. Calcium Fractions of Serum

/ . Total Calcium, Ultrafiltrable Calcium and [CaProt]

Patients were selected for study on the basis of hypercalcemia, i.e., elevation in serum total calcium. As shown in Figure 32a, this elevation was significant (p < 0.001); mean [Ca] in the 30 studies (24 patients) was

3.35 ± 0.18 (2 SE)mM, as compared with 2.47 ± O.OSmM in the 21 nor- mals.

Total diffusible calcium was also increased (Fig. 32b), with means of

2.17 ± 0.1 3mM and 1.47 ± 0.06mM in the cancer patients and normals,

respectively (p < 0.001). Of the serum total calcium, 64.8 percent was

thus ultrafiltrable, as compared with 59.8 percent in normals. In contrast

to cirrhotics (Secfion VII), this difference was not significant.

As seen in Figure 32c, average [CaProt] was significantly (p < 0.02)

increased in the cancer patients, with means of 1 . 1 8 ± 0. lOmM and 1 .00

± 0.09mM in cancer and normals, respectively. This finding is also in sharp contrast to that observed in cirrhotics (Fig. 22).

^The collaboration of Dr. Carlos Guzzo and the Oncology Division of the Medical Services

in these studies is gratefully acknowledged.
270 ION-SELECTIVE ELECTRODES

4.0-

3.5-

(A)

SERUM

TOTAL CALCIUM

^ NORMAL CANCER

(21) (30)

2.4710.08 3.3510.1 p< 0.001

3.5

3.0

2.5

2.0-

1.0 05-

(B)

ULTRA FILTRATE

TOTAL CALCIUM

(21) (30) .4710.06 2.1710.13 p< 0.001

(C)

[CaProtJ

2.5-

2.0-

1.5-

1.0-

0.5

0-1 1 NORMAL CANCER

(21) (30)

1.0010.09 1.18 1 0.10 p<0.02

Figure 32. (a) Total calcium concentrations (EDTA method) in sera from 21 normal subjects and 24 patients with malignancy (30 studies), (b) Total calcium concentrations in serum ultrafiltrates. (c) Calculated concentrations of protein-bound calcium [CaProt]. In

this and subsequent figures, enclosed boxes represent mean values ±2 standard errors.

2. [Ca^^]and[CaR\

Serum ionized calcium was also significantly (p < 0.001) elevated in the cancer patients, with a mean value of 1.51 ± 0.1 OmM as compared with

1.16±0.02mM in normals (Fig. 33). Variability in [Ca++] was great,

however, ranging from 1.13 to 2.14mM; in 7 studies (6 patients), serum

[Ca++] values were within the normal range. On the average, the per- centage increase (30 percent) in [Ca++] was similar to that for total calci- um (36 percent).

Mean [CaR], shown in Figure 33b, was also significantly increased in the cancer patients, to about twice the normal value: 0.66 ±0.1 OmM

and 0.32±0.06mM, respectively (p< 0.001).

3. Relative Values for [Ca^^], [CaProt] and [CaR]

The relative contribution, in percent, for each of the 3 calcium fractions

for both normals and cancer patients are shown on triangular coordinates

in Figure 34. In the latter group, [Ca++] constituted, on the average, 45.

1

± 2.0 percent of the total calcium, similar to the value 47. 1 ± 1.7 percent
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 271

SERUM

IONIZED CALCIUM

[CaR]

mM

2.2-

2.0-

1.8

1.6

1.4

1.2-1

1.0-

t

NORMAL CANCER

y (21) (30)

.1610.02 1.51 i 0.10 p< 0.001

mM

1.2

1.0-

0.8-

0.6-

0.4

0.2

•V

V

NORMAL CANCER

(21) (30)

0.32i0j06 0.6610.10

p< 0.001

Figure 33. (a) Serum ionized calcium concentrations [Ca++] in 21 normal subjects and 24

patients (30 studies) with cancer and hypercalcemia, (b) Diffusible calcium complex

concentrations [CaR], calculated as the difference in ultrafiltrate total calcium (EDTA

method) and ultrafiltrate ionized calcium concentrations.

in normals. Thus, while [Ca++] was significantly increased on the ab- solute scale, that fraction as [Ca + + ] was normal. In the cancer patients,

[CaProt] average 35.0 ± 2.2 percent of the total, significantly (p < 0.01)

less than the value 40.2 ± 2.8 percent in normals. Thus, although mean

[CaProt] was increased on an absolute scale in the cancer patients, its fractional contribution to the total was significantly reduced. [CaR]

averaged 20.0 ±2.8 percent of the total calcium in cancer, significantly

(p < 0.00 1 ) higher than that ( 1 2.7 ± 2.2 percent) in normals. Mean [CaR] was thus increased in relative as well as absolute terms.

B. Serum Proteins

Serum total protein, albumin and globulin levels are shown in Figure

35. As may be seen by comparison with Figure 25, mean values for the
272 ION-SELECTIVE ELECTRODES

[Co**] = 100%

100

[CaR] = l007o 100 40 60

[CaProt]

100 LCaProt]= 100%

Figure 34. Relative contribution, in percent, of each of the 3 calcium fractions of serum

in 21 normal subjects (closed circles) and 24 patients (30 studies) with cancer and

hypercalcemia (open circles). cancer patients were almost identical to those observed previously in cir- rhotics. Mean total protein was 65.2 ±3.8 g/1, significantly less than the

value of 72.3 ± 2.2 g/1 in normals (p < 0.01). Reduction in total protein

(A)

SERUM

TOTAL PROTEINS

gm/l

ICX)

90 H

80

70 H

5040-

•

• •

•

•••

••

• •

•

•X-

••

/ NORMAL CANCER

(21) (30) 72.312.2 65.21 3.e p<O.OI

(B)

SERUM ALBUMIN

gm/l60

50-

40-

30-

20

10-

0 NORMAL CANCER

(21) (30)

47.3* 2.2 30.313.0 p< 0.001

(C) SERUM GLOBULINS

gm/l80-

60-

50-

40-

30

20

10

•••

•••

^ NORMAL CANCER

(21) (30) 29.012.0 34.814.9

p<O.OI

Figure 35. Serum total protein (A), albumin (B), and globulin (C) concentrations in 21 normal subjects and 24 patients (30 studies) with cancer and hypercalcemia.
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 273 was due to marked reduction in serum albumin, with means of 47.3 ±

2.2 g/1 and 30.3 ±3.0 g/1 in normals and cancer patients, respectively (p <

0.001). As in cirrhotics, mean serum globulin level was significantly (p <

0.01) increased, with respective values of 25.0 ± 2.0 g/1 and 34.8 ±4.5 g/1 in normal and cancer. C. Relation of [Ca++] to Serum [Alb] and [Ca]

As may be seen in Figure 36, there was no apparent relation between serum ionized calcium concentration and serum albumin level in the cancer patients. This finding was similar to that observed in both normals

and patients with cirrhosis (Fig. 26b).

2.5n

2.0- o o

oo _

1.5-

mM

1.0

95 % Normal

[Co-]

Confidence Interval

0.5-

• = Normal

o = Cancer 0 1 1 1— 1 r— 1 10 20 30 40 50 60

SERUM ALBUMIN

(gm/l ) Figure 36. Relationship between serum ionized calcium and albumin concentration in 21 normal subjects and 24 patients (30 studies) with hypercalcemia of malignancy. In contrast to both normals and cirrhotics, who showed no relation

between serum ionized and total calcium concentrations, we find a strik- ing difference in the hypercalcemia of malignancy. As shown in the upper

half of Figure 37, [Ca+ + ] was linearly related to [Ca]; the slope of the

function was 0.45 and the intercept was nearly zero. This is remarkably

similar to the observed relation between [Ca+ +

] and [Ca] seen upon dilu- tion or addition of calcium to normal serum in vitro (Section IV). The

latter data are shown for comparison in the lower half of Figure 37.
274 ION-SELECTIVE ELECTRODES

mM

HYPERCALCEMIA OF MALIGNANCY

3-, [Ca**] = 0.450 [Co]

(r = 0.78)

2 H

o

I -

TOTAL CALCIUM

mM

NORMAL SERUM

[Ca**J « 0.473 [Co]

( r«0.98)

I 2 3

TOTAL CALCIUM

mM

Figure 37. (a) Relation of serum ionized calcium [Ca++] and total calcium [Ca] concentrations in 30 studies of 24 patients with cancer and hypercalcemia, (b) Relation of serum

ionized and total calcium concentrations upon dilution of normal serum in vitro with NaCl or addition of CaCl2-NaCl, over the same [Ca] concentration range encountered in the cancer patients. pH, temperature and ionic strength are constant as described in Section IV. Note particularly the slope of 0.47. In other words, the ionized calcium

values observed in the cancer patients were almost exactly those expected if we had simply added calcium to normal serum in a test tube. The presumed

significance of this will be noted below.

D. Relation of Total Calcium to [Alb] and [CaProt]

The relation between serum total calcium and albumin levels in the

hypercalcemia of malignancy is shown in Figure 38. Data from normal
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 275

5-1

4-

SERUM 3-

TOTAL

CALCIUM

(mM) 2"

I -

y = 1.61 0.0I9X

(r= 0.94)

• = Normal

A = Cirrhosis o= Cancer

10 —1—

20 30 40 50 60

SERUM ALBUMIN

(gm/l )

Figure 38. Relationship between serum total calcium and albumin concentrations in 30

studies of 24 patients with cancer and hypercalcemia. Note that there is no strong correlation, in contrast to findings in normals and patients with cirrhosis. Data for the latter 2 groups are from Figure 28. subjects and patients with cirrhosis (Fig. 28) are also shown for comparison. In contrast to the latter groups, there was no strong correlation

between [Ca] and [Alb]. This, in. itself, suggests the possibility of signifi- cant binding to serum globulins in cancer. Another striking difference in these patients was the relation of

protein-bound calcium to serum albumin level. As noted in Figures 32

and 35, serum total calcium was significantly increased while serum albu- min was significantly reduced in the cancer patients. Thus, it was not sur- prising to find that, in comparison with normals, a given [CaProt] level in cancer was achieved at a higher total calcium level. This is indicated in Figure 39, in which the curve for cancer patients was displaced to the

right. Also, it is evident from Figure 39 that, in contrast with normals and

also cirrhotics (Fig. 29), change in serum total calcium was not accounted

for by corresponding change in [CaProt]. The lower slope (0.44) for cancer patients in Figure 39 reflects the fact that there was also a proportionate increase in ionized calcium (Fig. 37). Clearly, we are dealing with

a problem quite different from that in cirrhotics.
276 ION-SELECTIVE ELECTRODES

2.0

• NORMAL

o « CANCER

[CaProt]

mM

L5

1.0

05

1.0 2.0 3.0 4.0 SERUM TOTAL CALCIUM mM

5 0

POOLED DATA

[CaProt]

mM

1.0 2.0 3.0 4.0 5.0 SERUM TOTAL CALCIUM mM

Figure 39. Relationship between protein-bound calcium [CaProt] and serum [Ca] concentrations in 21 normal subjects and 30 studies of 24 patients with cancer and

hypercalcemia. The pooled data for normals are from Figure 29. Note that the curve for hypercalcemia cancer patients, with reduced serum albumin levels, is displaced to the

right with a slope less than half that observed in normals.

E. Fractionation of [CaProt]

This difference is further illustrated in Figure 40, in which [CaProt] is given as a function of serum albumin. The previous data from normal subjects are shown again for comparison. In contrast to cirrhotics, in whom

there was a strong linear relationship with an intercept of about zero and

a slope nearly identical to that in normals (Fig. 27), we find no strong cor-
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 277

relation in the cancer patients. The slope was apparently less than normal

and there was a sizable intercept on the vertical axis, suggesting that these

patients may have a substantial fraction of protein-bound calcium in the

globulin fraction. If this were the case, the slope of the function would not

tell us anything about that fraction bound to albumin because, as it so happens, serum albumin and globulin were inversely related in these patients.

[CaProt]

mM

2.0

1.5

1.0

0.5-

NORMAL

o- CANCER

o oy°oo o o

o o

o

y • O II ^ 0 0I9X

10 —I20 —I

30 —I

40 50 60

SERUM ALBUMIN

( qm/ I

)

POOLED DATA

[CaProt]

mM

2.0-1

1.5-

10-

05- • y «0 II - 0.0I9X (r.o.ee) oy. 0 78 + 0.0I2X

( f ' 0.66 ) 10 20 30 40 50 60

SERUM ALBUMIN

( gm/ I

)

Figure 40. Relationship between protein-bound calcium [CaProt] and serum albumin

concentrations in 30 studies of 24 patients with cancer and hypercalcemia. Normal

data from Figure 27 are shown for comparison. Note the lack of a strong correlation among the cancer patients. The pooled-data function below suggests that a significant fraction of protein-bound calcium is in the globulin fraction.
278 ION-SELECTIVE ELECTRODES

How, then, can one tell how much is bound to albumin and how much

to globulin? Studies in the past [22] with fractionated serum proteins have

suggested that albumin normally accounts for about 80% of the

protein-bound calcium, while globulins account for the remaining 20%.

But is this the case in vivo and particularly in cancer patients? (As noted

above. Figure 28, our data in normals would suggest that about 1 1 percent

of [CaProt] is in the globulin fraction).

An estimate of the relative binding to albumin and globulin was obtained as follows: Let the observed [CaProt] concentration at any given

total calcium and albumin level represent the sum of calcium albuminate

and calcium globulinate:

[CaProt] = [CaAlb] + [CaGlob] (21)

Both [CaAlb] and [CaGlob] are unknown. Albumin and globulin levels are known, however, and at any given calcium level Equation (21) may be

rewritten with two new unknowns, x and z'. [CaProt] = jc [Alb] + z[Glob] (22)

where [Alb] and [Glob] are in g/1 and:

[CaAlb]

[Alb]

(mM/g) (23a)

Rearrangement of Equation (22) yields:

[CaProt] ^ [Glob]

[Alb]

^

[Alb] (24)

A . . w c [CaProt] . , [Glob] , , ,

• If X and z are constant, a plot of —

^w\^^ agamst

^-^^^^ should yield a straight line with intercept and slope equal to the albumin {x) and

globulin (z) binding constants, respectively.

The observed relationship was indeed linear, as shown in Figure 41. In- dividual data are shown on the top; on the bottom the data were pooled by

increments in the [Glob] /[Alb] ratio in an effort to obtain the best esti- mates of the functions.

In normals, the intercept indicated that, on the average, 0.0167mM cal- cium was bound to each gram of albumin, while the slope indicated that

less than half as much was bound to each gram of globulin, 0.0079mM/g.

In cancer patients, at higher total and ionized calcium levels, the respective constants were 0.0256mM/g and 0.0133mM/g, respectively. Comparison of respective intercept and slope values for the two groups sug-
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 279

0.08

0.06- [CaProt]

[Alb]

(mM/gm)

0 02-

• « NORMAL

©• CANCER

o 8

10 20 3 0 [Glob]

[Alb]

POOLED DATA

0 08 -I • ' ' 0.0167 + 0.0079 X (r-0.97) [CoProt]

(mM/gm)

0 02

o y-O 0256 -!> 0.0133

X

r.0.95)

10 2.0 3.0 [Glob]

[Alb]

Figure 4L Plots of Equation (24) for estimation of albumin and globulin binding-constants as described in the text. Intercept values on the bottom indicate that in normals and

cancer patients, respectively, an average of 0.0167mM and 0.0256mM calcium were bound to each gram of albumin. Slope values indicate that in normals and cancer patients, respectively, an average of 0.0079mM and 0.0133mM calcium were bound to each gram of globulin.

gests that the values in the cancer patients are about those predicted from

the mass-law equation at the higher Ca++ levels present in these patients.

Having obtained the necessary constants, and knowing the albumin and

globulin levels in each subject, the relative binding of albumin and globulin is readily calculated. Thus, in normals:

[CaAlb] = 0.0167 [Alb] [CaGlob] = 0.0079 [Glob] (25a)

[Alb]^-47.3 g/1 [Glob] J= 25.0 g/1 (25b)

[CaAlb] s = 0.79 mM [CaGlob]x=0.20 mM (25c)
280 ION-SELECTIVE ELECTRODES

and calculated mean [CaProt] was: (0.79 + 0.20) = 0.99mM. The latter value is in close agreement with the observed mean [CaProt] value of

l.OOmM (Fig. 32).

Similar calculations in the cancer patients, in whom there was signifi- cant reduction in albumin and significant increase in globulin concentrations (Fig. 35), yielded mean [CaAlb] and [CaGlob] levels of 0.78mM

and 0.44mM respectively. Their sum, 1.22mM, was also close to the mean observed [CaProt] concentration of 1.1 8mM (Fig. 32).

As summarized in Figure 42, our data in normals indicate that about 81 percent, calculated for each individual subject, of protein-bound calcium

is bound to albumin and about 19 percent to globulins. These values

are very close to those estimated by Neuman and Neuman [22], and

are the reason that [CaAlb] was assumed to equal 80 percent of [CaProt]

in Section IV above.

NORMAL CANCER

(HYPERCALCEMIA )

81.1% CaAlb

CaProt = 18.9% CaGlob

66.5 % CaAlb

CaProt = 33.5 % CaGlob

( p< 0.01 ) Figure 42. Average values for the relative binding of calcium to albumin [CaAlb] and

globulin [CaGlob] in 21 normal subjects and 30 studies of 24 patients with cancer and

hypercalcemia. Values were derived from data obtained in Figure 41. In the cancer patients, the calculated percentage for calcium albu- minate was 66.5 percent, significantly (p < 0.01) less than in normals,

while calcium globulinate accounted for 33.5 percent of [CaProt], significantly higher than in normals (p < 0.01). These values for cancer patients are in sharp contrast to the findings in cirrhotics. Thus, while both groups

of patients had almost identical albumin and globulin levels (Figs. 25 and

35), cirrhotic patients showed no detectable binding of calcium to serum

globulins (Fig. 27). It would therefore appear that there are important

qualitative differences in the serum globulins of these two groups of patients. This problem is still under study.

Since the above calculations in normals were based on a regression

consisting of only 3 points (Fig. 41), an effort was made to check on the

validity of the calculated [CaAlb] value [0.79mA^, Eq. (25c)]: mean ^ CaAlb the normals was calculated from Equation (10):

^, _ [Ca-](4Alb]- [CaAlb])

^^^^'^ [CaAlb] ^^^^
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 281

Assuming that the molecular weight of albumin is 69,000 and n = 8.4 (Fig.

18), substitution of: [Ca++]^ =1.16mM (Figs. 23 and 33)

LAlb]^ ==47.3 g/1 (Fig. 35)

[CaAlb]^ =0.79mM (Eq. 25c)

for the 21 normal subjects yielded a mean A^caAib value of

7.29x10-3 (pA:=2.14). This is in close agreement with the value

(p/C' = 2.18) obtained in Figure 18 upon addition of calcium to normal serum in vitro, suggesting that the values obtained in Figure 41 for normals are reasonably accurate.

F. Summary

From these data, a model (Fig. 43) has been constructed for serum total calcium and each of the three calcium fractions: [Ca++], [CaProt] and

[CaR]for both normals and patients with malignancy and hypercalcemia.

In normals, serum total calcium varied from about 2.25-2.75mM (95%

confidence interval). Regardless of the serum total calcium, serum ionized

calcium was maintained at about 1.1 6mM. Mean [CaR] was also essentially constant at about 0.3mM. Variation in total calcium was almost entirely accounted for by corresponding variation in protein-bound calcium.

Of this, about 80 percent was bound to albumin and 20 percent to globulins.In sharp contrast, in patients with malignancy and hypercalcemia, in- crease in serum total calcium was accompanied by a progressive rise in ionized calcium at a constant fractional rate representing 45 percent of the

total. This fraction was similar to that observed in normal subjects in vivo

(Fig. 12) and upon addition of calcium to normal serum in vitro (Fig. 37).

Both [CaProt] and [CaR] were significantly increased in absolute terms. [CaProt] increased with increasing total calcium at a constant fractional

rate of about 44 percent (Fig. 39). Of the [CaProt], that fraction bound to globulin was increased in both absolute and relative terms, while the rela- tive binding to albumin was significantly reduced to about 66 percent of

the [CaProt] level. The latter finding is in marked contrast to cirrhotic patients with comparable levels of albumin and globulin. In these cancer patients, it would appear that the circulation has been

presented with an excessive calcium load and that the resulting distribu- tion in serum is that predicted physicochemically. Since the distribution

of calcium in serum is subject to several variables, it may prove rather dif- ficult to extrapolate from the regressions established for the group to the

individual patient. Nevertheless, our data appear compatible with the be-
282 ION-SELECTIVE ELECTRODES

SERUM

[Ca]

mM

Figure 43. A model for the state of serum calcium in normals and in the hypercalcemia

of malignancy.

lief [68] that the hypercalcemia may be the result of excessive parathormone-like material in at least some of these patients. IX. Summary

An attempt has been made in this chapter to summarize some of our

studies with ion-exchange calcium electrodes and to develop a reasonably

coherent thesis concerning some of the complex physicochemical factors

governing serum calcium in man. From data obtained in various aqueous

salt solutions, in sera and in ultrafiltrates, models have been developed for the state of serum calcium in normals, in patients with cirrhosis, and in the

hypercalcemia of malignancy. The binding of calcium to the serum

proteins has been found to obey the mass-law equation and a dissection

of the relative contributions of albumin and globulin has been achieved by

a simple regression analysis apparently not recognized previously.

There is no doubt that these electrodes can provide very high quality

data in many biologic systems. Space has not permitted a discussion of all the types of studies which have been made. The development of a Ca++

activity scale by Bates (Chapter 6) is an important advance in the applica-
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 283

tion of these electrodes to many biological problems. It is anticipated that meaningful thermodynamic data will soon be forthcoming concerning cal- cium transport across various biologic membranes.

While these electrodes are by no means perfected — they can be

quite frustrating at times — it should be remembered that ion-exchange

electrode technology is still in its infancy. Further improvements will un- doubtedly enhance their general usefulness. On-line monitoring, for ex- ample, is quite feasible today and telemetering cannot be far behind.

Should it prove possible to develop suitable Ca++ microelectrodes,

Pandora's Box will become so large that physiologists may not come out

of it in this century. In any case, it seems clear that we are on the

threshold of a bright new era in the field of calcium metabolism. The elec- trode, coupled with recent advances in peptide chemistry and immunology, will greatly enhance our present understanding of calcium metabolism.

X. Acknowledgment

This work was supported by U. S. Public Health Service research

grants AM-07417, AM-10307 and AM-13357, by Training Grant No.

AM-05424, National Institute of Arthritis and Metabolic Diseases,

and by Research Career Development Award K3-GM-1 1-386, National

Institute of General Medical Sciences, U.S. Public Health Service. The

author is indebted to Dr. James W. Ross, Jr., for his assistance in electrode fabrication and many helpful suggestions, to I. Rasmusen,

L. Anderson, S. Lee, S. Sullivan and D. Alvarez for their able technical

assistance, to Mr. B. T. O'Neil for his assistance with the illustrations,

and to Miss C. Benjamin for her able secretarial assistance. The efforts of

several colleagues who participated in some of these studies are also

gratefully acknowledged: Dr. Joel Jacknow, Dr. Andre Blum, Dr. Carlos

Guzzo and Dr. Roger Dawkins.

XI. References

[ I] Moore, E. W., in Glass Electrodes for Hydrogen and Other Cations: Principles and

Practice, G. Eisenman, Ed., Marcel Dekker, New York, 1 967, p. 4 1 2. [2] Moore, E. W., in Bioelectrodes, W. Feder, Ed., Ann. N. Y. Acad. Sci. 148: Art. 1,93

(1968).

[3] McLean,F.C. and Hastings, A. B.,J. Biol. Chem. 107,337 (1934).

[4] McLean, F. C. and Hastings, A. B.,J. Biol. Chem. 108, 285 ( 1 935).

[5] McLean, F. C. and Hastings, A. B., Amer.J. Med. Sci. 189,601 (1935).

[6] Ross, J. W., Jr., Science 156, 1378(1967).

[7] Fosbinder, R. L, J. Amer. Chem. Soc. 51 , 1345(1929).

[8] Joseph, N. R.,.l. Biol. Chem. 126,389(1938).

[9] Greenberg, D. M., in Advances in Protein Chemistry, Vol. I, M. L. Anson and.I. T.

Esdall, Eds., Academic Press, New York, 1944, p. 121.

[ 10] Sollner, K., J. Amer. Chem. Soc. 65, 2260 (1943). [II] Abrams, L M. and Sollner, K., J. Gen. Physiol. 26. 369 ( 1 943). [12] Sollner, K. and Neihof, R. A., Arch. Biochem. Biophys 33, 166(1951).

348-381 O 69—20
284 ION-SELECTIVE ELECTRODES

Gregor, H. P. and Sollner, K.J. Amer. Chem. Soc. 58, 409 (1954). Carr, C. W., in Electrochemistry in Biology and Medicine, T. Shedlovsky, Ed., John

Wiley and Sons, New York, 1955, p. 266. Gregor, H. P. and Schonhorn. H., J. Amer. Chem. Soc. 79, 1507 (1957); ibid., 81, 391 1 ( 1 959); 83, 3576 (1961). Eisenman, G., Rudin, D.O., and Casby, J. U., Science 126, 831(1 957). Truesdell, A. H. and Christ, C. L., in Glass Electrodes for Hydrogen and Other Cations: Principles and Practice, G. Eisenman, Ed., Marcel Dekker. New York, 1 967,

p. 293. Raaflaub,J.,Z. Physiol. Chem. Hoppe-Seylers 288, 228 (1951). Rose, G. A., Clin. Chim. Acta2, 227 ( 1957). Walser, M., Anal. Chem. 32, 7 1 1 ( 1 960). Walser. M., J. Clin. Invest. 40, 723 ( 1 96 1 ). Neuman, W. F. and Neuman, M. W., The Chemical Dynamics of Bone Mineral, Univ. of Chicago Press, Chicago, 1958, p. 12, pp. 1-38. Copp, H.. D., in Advances in Internal Medicine, Vol. XIV, I. Snapper and G. H.

Stollerman, Eds., Year Book Medical Publishers, Chicago, 1968, p. 55. Albright, F. and Reifenstein, E. C, The Parathyroid Glands and Metabolic Bone

Disease, Williams and Wilkins, Baltimore, 1 948. Nordin, B. E. C. and Smith, D. A.. Diagnostic Procedures in Disorders of Calcium

Metabolism, Little, Brown, Boston, 1965. Fourman, P. and Royer, P., Calcium Metabolism and The Bone, Blackwell Scientific Publications, Oxford, 1 968. Rona, P. and Takahashi, D., Biochem. Z. 31, 336 ( 1 9 1 1 ). Marrack,J. and Thacker, G., Biochem. J. 20, 580 ( 1 926). Watchorn, E. and McCance, R. A., Biochem. J. 26, 54 (1932). Greenberg, D. M. andGunther, L.,J. Biol. Chem. 85, 491 (1930). Nicholas, H. O., J. Biol. Chem. 97, 457 (1932). Dillman, L. M. and Visscher, M. B., J. Biol. Chem. 103, 79 1 (1933). Morison, R. S., McLean, R., and Jackson, E. B., J. Biol. Chem. 122, 439 ( 1 937). Hopkins, T., Howard, J. E., and Eisenberg, H., Bull. Johns Hopkins Hosp. 91, 1 (1952). Toribara,T. Y., Terepka, A. R.,and Dewey, P. A., J. Clin. Invest. 36, 738 ( i 957). Walser, M., J. Cell. Comp. Physiol. 55, 245 (1960). Loken, H. F., Havel, R. J., Gordan, G. S., and Whittington, S. L.,J. Biol. Chem. 235, 3654(1960).

Prasad. A. S. and Flink. E. B.,J. Lab. Clin. Med. 51, 345 ( 1 958). Prasad, A. S., A.M.A. Arch. Int. Med. 105,560(1960).

Breen, M. and Freeman, S., Clin. Chim. Acta 6, 1 8 1 ( 1961 ). Moore, E. W. and Makhlouf, G. M., Gastroenterology 55, 465 ( 1968). Moore, E. W. and Ross, J. W., Jr., J. Appl. Physiol. 20, 1332(1965).

Harned, H. S. and Owen, B. B.. The Physical Chemistry of Electrolytic Solutions, Reinhold, New York, 1963, p. 595.

Klotz, L M., Chemical Thermodynamics, Prentice-Hall. Englewood Cliffs, N. J., 1950, p. 329. Robinson, R. A. and Stokes, R. H., Electrolyte Solutions. Butterworth, London,

1959, p. 438. Bachra, B. N., Dauer, A., and Sobel, A. E., Clin. Chem. 4, I07( 1 958). Gornall, A. C, BardavilKC. J.,and David, M. M.,J. Biol. Chem. 177,751 (1949). Moore, E. W., J. Clin. Invest. 45, 1047 (1966) (Abstract).

Sill6n, L. G. and Martell, A. E., Stability Constants of Metal-Ion Complexes, Special Publication No. 1 7, The Chemical Society, London, 1964, p. 478.
BIOLOGICAL STUDIES WITH CALCIUM ELECTRODES 285

[50] Fanconi, A. andRoscG. A., Quart. J. Med. 27, 463 ( 1 958). [51] Nakayama, F. S. and Rasnick, B. A., Anal. Chem.39, 1022 (1967). [52] Garrels, R. M., in Glass Electrodes for Hydrogen and Other Cations: Principles and

Practice, G. Eisenman, Ed., Marcel Dekker, New York, 1 967, p. 349.

[53] Bates, R. G., Determination of pH, John Wiley and Sons, New York, 1964, p. 275. [54] Moore, E. W. and Wilson, D. W., J. Clin. Invest. 42, 293 ( 1 963). [55] Yendt, E. R., Connor, T. B., and Howard, J. E., Bull. Johns Hopkins Hosp. 96, 1 (1955). [56] Ettori,J.andScoggan,S. M., Nature 184, 1315 (1959). [57] Scatchard,G., Ann. N. Y. Acad. Sci. 51, 660 ( 1 949). [58] Klotz, 1. M., Arch. Biochem. 9, 109(1946).

[59] Katz, S. andKlotz, I. M., Arch. Biochem. 44, 35 1 (1953). [60] Tanford, C, Physical Chemistry of Macromolecules, John Wiley and Sons, New

York, 1961, pp. 526-586.

[61] Schultze, H. E. and Heremans, J. F., Molecular Biology of Human Proteins, Elsevier, Amsterdam, 1966, p. 182. [62] Moore, E. W. and Blum, A. L.,J. Clin. Invest. 47, 70a (1968) (Abstract). [63] Ruch, T. C. and Patton, H. D., Physiology and Biophysics, W. B. Saunders,

Philadelphia, 1965, p. 943. [64] Held, D., Fend, V., and Pappenheimer, J. R., Fed. Proc. 22, 332 ( 1 963)( Abstract). [65] Dawkins, R. L. and Moore, E. W., Clin. Res. 17, 283 (1969) (Abstract). [66] Tashjian, A. H., Jr., Levine, L., and Munson, P. L., Endocrinology 74, 244 (1964). [67] Moore, E. W., presented in part before The Gastroenterological Research Forum,

American Gastroenterological Association, Washington, D. C, May 1969; (Abstract), Gastroenterology (in press). [68] Bower, B. F. and Gordan, G. S., Ann. Rev. of Medicine 16, 83 (1965).

CHAPTER 8

ION-SELECTIVE ELECTRODES IN BIOMEDICAL

RESEARCH

Raja N. Khuri

Department ofPhysiology

American University ofBeirut

Beirut, Lebanon

I. Potentiometry in Biological Systems

Potentiometry consists of the measurement of the electromotive force

of a galvanic cell (composed of two half-cells). Direct analytical potentiometry has been widely applied in the measurement of ionic activities of

many ionic species of a wide variety of biological systems. The deter- mination of ion activity by the electrometric method offers some special

advantages over such methods as colorimetric analysis, flame photometric analysis, compleximetric and other chemical methods in the measure- ment of ions in biological systems.

The indicator half-cell consists of an ion-selective electrode predominantly sensitive to a specific ion species, the so-called primary ion in question. The fact that ion-selective electrodes measure ion activities rather than concentrations is not a disadvantage in biological work, since

biological phenomena are functions of ionic activities rather than concentrations. The measurement of ionic activity is all the more significant

because ion-complexing and ion-association phenomena are common in biological systems. Ion-sensitive electrodes can be adapted for continu- ous in situ measurements [1 ,2] which is superior to the intermittent sampling techniques that the other methods employ. The most unique ad- vantage of ion-sensitive electrodes is their ability to perform a direct measurement of ionic activity in a biological system in situ. This applies to both the macro and microscales. The latter, microelectrode analysis, is a

field of great importance in fundamental biological research.

Biological systems are quite complex. Although water is the principal

biological solvent, the aqueous media of living systems are mixed elec- trolyte solutions that often contain colloidal polyelectrolytes. Even the

microscopic units of structure and function, the single cells, are not homogeneous and consist of several distinct phases.

A. Mixed Electrolyte Solutions

Biologic aqueous solutions are not simple solutions but usually consist

of a mixture of several salts. Mixed ionic solutions require highly selec- 287
288 ION-SELECTIVE ELECTRODES

tive electrodes to measure a specific ion in question in the presence of all other ions. Only electrodes of pH-sensitive glasses fully meet this require- ment. Sodium and potassium are two prevalent cations in many biologic solutions. The potential of a cell incorporating Na+-sensitive glass electrode

NASii-18 may be described by the following equation: = El, + /?r/F In [

( Na+ ) + k^^.n (

) + ^^a-K (K+ ) ] (1) where R, T and F are the gas constant per mole, the temperature in degree

Kelvin, and the Faraday constant, respectively. is the measured

potential and E^, the standard potential of the sodium electrode. (Na+)

is the activity of the sodium ion. The selectivity constants of the glass

electrode ta H+ and K+ ions relative to Na+ ion are A:Na-H and A:Na-K- Electrodes of NASii-18 glass yield values of ^Na-H~10 and ^Na-K of

0.01-0.001. Thus, in neutral mammalian extracellular fluid with a concentration of 5 X lO-^M the sodium glass electrode is essentially sensitive

to the Na+ ion only and Equation (1) reduces to: E^,= El,-hRTlF\n{N2i^) (2) The so-called "cation-sensitive" glasses are characterized by a selectivity

order:

H+> K+> Na+ »Ca++

In neutral biologic fluids electrodes of these glasses have a predominant

selectivity for the K+ ion and the electrode potential may be described by

the following equation:

E^ = Ei + RTIF\n [{K^) + k^_^,{Na^)] (3) Such an electrode is sensitive to both K+ and Na+ ions. When a

"cation-sensitive" electrode is paired with a sodium-sensitive electrode,

the potential of the galvanic cell composed of the two glass electrodes is obtained by subtracting the half-cell Equation (2) from (3): E^-t^a-EK-Na+RJ Ir In. ((Na+) J The two-glass electrode cell described by Equation (4) measures a concentration ratio since the activity coefficients cancel out in the ratio. Garrels [3] used the K-Na glass electrode cell for measuring these cations

in sea water. Friedman, et ai [1] used the all-glass cell to monitor the

cations in blood. Khuri, et ai [4,5] and Lev [6,7] used the pair of Na and

K-glass microelectrodes in biological research. The all-glass cell employed
BIOMEDICAL RESEARCH 289

by Khuri, et al. is shown in Figure 1. The use of a pair of two glass

electrodes with different selectivity constants is a useful technique in Na*- reference K""- indicator

I

I Sample

Figure 1 . K+ microelectrode — N a+ microelectrode cell (for K/N a measurement).

Studies of mixed electrolytes. It is a cell without a liquid-liquid junction.

There is no leakage of salt-bridge electrolyte into the test sample, and as

stated above, the method may be independent of activity coefficients. In

solutions of mixed salts, one can under certain conditions speak of

"mixed" activity coefficient for a mixture of two salts with a common

anion. The concentration of uni-univalent salts in mammalian body fluids

is about 150 mM, a value which is well above what is generally regarded

as dilute solutions. This is one of the factors that contributes to the dif- ferences between ionic activities and concentrations in biologic solutions. B. Colloidal Solutions

Biologic solutions contain variable but significant amounts of colloidal

polyelectrolytes. Protein constitutes the major organic polyelectrolyte.

Mammalian plasma has 6-7 g protein/ 100 ml (referred to as g%), while the

intracellular protein varies over a wide range (8-36 g%). The intracellular

protein is in the form of a colloidal suspension. At the physiologic pH of

their respective media, both the intracellular and the extracellular
290 ION-SELECTIVE ELECTRODES

proteins are anionic and may potentially possess cation exchange properties. The cation exchange properties of protoplasmic polyelectrolytes and

their role in the distribution of Na+ and K+ across cell membranes has not been elucidated.

Ion-selective electrodes are useful analytical tools for the study of the

protein binding of ions. However, protein poisoning of electrodes is a common problem which is particularly serious in the case of the metallic

electrodes and the oxidation-reduction electrodes. Glass electrodes are

in general less susceptible to protein poisoning, but to avoid developing a protein coat on the electrode it is advisable to rinse the probe promptly

with a buffer standard.

C. The Liquid Junction Potential

The liquid junction potential exists at the junction of two different ionic

solutions. A junction between two dissimilar electrolyte solutions is made

up of a mixture of ions in the process of traversing the boundary. If the

ions migrate with different mobilities, a spatial ionic separation results. In

the steady-state this chemical gradient across the boundary is balanced by

the liquid junction potential. In practical potentiometric analysis, the liquid junction exists between

the salt bridge component of the reference half-cell and the calibrating

standard or test sample. Bates [8] emphasized that it is the "residual

liquid junction potential" which is significant. This is the difference

between the potential at the salt bridge — standard junction and the

potential at the salt bridge — test solution junction. The magnitude of

the liquid junction potential is often very difficult or even impossible to determine. Thus it is a major uncertainty in potentiometric analysis since

the value of the residual liquid junction contributes to the apparent ionic

activity of the species in question.

There are several factors which affect the liquid junction potential. The

first is the geometry of the junction itself In biological work the most

widely used reference half-cell is one that incorporates a KCl-filled Ling

and Gerard [9] micropipette for a salt bridge. Although KCl will diffuse

into the tissue or test sample, the flow of salt bridge electrolyte is highly

restricted by the very small caliber of the tip of the micropipette. To

prevent the flow of concentrated KCl resulting from hydrostatic forces, one of several approaches may be undertaken. The simplest would be to maintain the salt bridge micropipette in the horizontal position. Another

would be to dissolve the KCl in 1-2% agar and fill the micropipette with

the hot agar. This serves both to eliminate the hydrostatic forces on the

aqueous phase as well as to impede the diffusion of KCl in the viscous

agar. A third technique consists of dipping an already filled internal capillary microelectrode in the salt bridge solution in the same manner as the
BIOMEDICAL RESEARCH 291

Radiometer pH cell reported by Siggaard- Andersen [10]. The tip of the

KCl-filled micropipette often picks up organic matter following tissue

penetration. This may alter the tip potential and necessitates recalibration

of the cell. The author [11] mounts the reference micropipette into a holder shown in Figure 2 after the design of Grundfest, et al. [12]. This

micropipette holder allows the injection of KCl solution through the tip

following each tissue penetration. Thus a stable potential may be maintained at the tip, a fresh junction being reformed each time by the KCl in- jection.

Figure 2. Reference micropipette holder with injecting mechanism.

Of the factors that affect the residual liquid junction potential, a radical

change in ionic strength or pH of the solutions should be avoided. In

biological work these may be avoided by maintaining the pH and the ionic

strength of the standards close to the values of the unknowns in question.

The salt bridge solution itself certainly affects the potential that arises

at the junction between itself and the buffered standards or the unknown

solution. Concentrated KCl, 3M or saturated (4.2M), is the most widely

used. The choice of KCl is based on the fact that the ionic mobilities of

potassium and chloride are practically identical, thus minimizing the

liquid junction potential. In addition, a small junction potential is favored

by maintaining a salt bridge of high concentration in contact with the test sample. For 3M KCl the concentration ratio of the salt bridge/mammalian

extracellular fluid is about 200. Biological investigators have substituted

other salt bridges for the conventional concentrated KCl in order to avoid

contamination with KCl or the effect of KCl on proteins. Semple [13]

using a 0.1 52M NaCl salt bridge, found that it yielded a blood pH which was on the average 0.1 1 pH units lower than the pH obtained with a cell incorporating a concentrated KCl bridge. This difference probably

represents a significant residual liquid junction potential that arises on
292 ION-SELECTIVE ELECTRODES

substituting NaCl for the equitransferent KCl. Khuri, et al. [14] used an

equilibrium diffusate of plasma as a salt bridge for blood pH determinations. Except for the Donnan effect, the boundary that the colloid-free

plasma salt bridge forms with its own plasma is probably characterized by

equivalent ion migration in both directions. In an attempt to eliminate the liquid junction potential. Khuri and

Merril [15] performed a potentiometric study and found the blood pH

measured by a cell, which utilizes a sodium glass electrode as a reference

to the pH glass electrode (does not incorporate a liquid-liquid junction), to be identical with the pH measured with a saturated KCl salt bridge. This

suggests that concentrated KCl minimizes the liquid junction potential in blood as in simple solutions.

D. Biologic Standards

It is often advisable that biomedical workers prepare their own stan- dards for potentiometric analyses. In general, the standards used for

calibrating the galvanic cell are prepared by reliable gravimetric and volumetric methods. Ideally, a measurement by a non-potentiometric method

is both useful and of some comparative value.

For the calibration of pH-sensitive electrodes, for blood pH determinations, Khuri and Merril [15] used buffer standards containing 140 mM

NaCl in 5 mM Tris(hydroxymethyl-amino-methane) titrated with HCl to various pH values around neutrality. These buffers were initially and re- peatedly calibrated against three National Bureau of Standards buffers

whose pH values at 25 °C are 4.008. 6.865 and 7.413. The saline buffers

have an ionic strength, a composition, and pH values that are not very dis- similar from the plasma being measured. By bracketing the biologic un- known samples with such biologic standards, the residual liquid junction

potential may be minimized and the response time in going from standard

to unknown may be favorably reduced.

Standards for the calibration of ion-selective electrodes should be buff- ered to a constant and neutral pH. This is particularly important in the case of Na-glass and K-glass electrodes which are more sensitive to H+

than to either Na+ or K+ ions. The performance of several types of electrodes may be improved by

storage or conditioning in calibrating standards or dilute solutions of their primary ion. Following the exposure of ion-selective electrodes to solu- tions rich in protein or after their use in vivo, the electrodes should be

promptly rinsed and washed with appropriate calibrating standards.

The entire electrode cell assembly should be maintained at constant

temperature. Also, the measurements of standards and unknowns should

be carried out at the same temperature. For in vitro studies, all measure- ments could be carried out at room temperature or any arbitrary tempera-
BIOMEDICAL RESEARCH 293

ture which does not undergo significant fluctuations. But when undertaking potentiometric work in vivo, where body temperature is maintained at a constant value (37-38 °C in warm-blooded animals), the electrometric

cell and the calibrating standards must be maintained at body temperature.

E. "BlOELECTRODES"

Cellular membranes made up of anionic lipo-proteins often exhibit cat- ion exchange properties. Mueller and Rudin [16] studied the cation

exchange properties of the valinomycin membrane, a bimolecular

phospholipid membrane, and found it to be predominantly selective for

among the group la cations. In studies of the electrical potential of biological membranes and their

passive permeabilities to the cations, Ussing [17] concluded that the out- ward-facing membrane of the frog skin has a greater passive permeability

for Na+ than for K+. The inside membrane of the frog skin behaved as a potassium electrode, i.e., the membrane electrical potential difference was solely determined by the K+ ion concentration bathing it. Similarly,

the outside membrane behaved as a sodium electrode. The transepithelial

electrical potential difference may be simulated to two cation electrodes

in series. In contrast, Giebisch [18] found that both the luminal and

peritubular cell boundaries of the proximal tubular epithelium of Necturus kidney are depolarized by elevation of the K+ ion concentration. A

slope in excess of 50 mV for a decade change in potassium concentration was observed. Thus in the renal epithelium, both boundaries exhibit high

K+ selectivity and behave as potassium electrodes. Hodgkin, et al. [19,20] have shown that the resting potential across single muscle and

nerve fibers when plotted against the external concentration of potassium

exhibit a Nernstian response over a significant range of K+ concentration.

Thus, the plasma membrane of single muscle and nerve fibers exhibit

potassium electrode behavior.

II. In Vitro vs. In Vivo

Ion-selective electrodes have been widely used to measure ion activities in biologic media both in vitro and in vivo. Both applications have util- ized the full spectrum of electrode size from the macro to the ultramicro.

The demarcation between the macro and the microscales is quite arbitrary. For our purposes, we shall define the upper limit of the microscale

by the volume of an average aqueous drop, 50 /xl or an even smaller

volume of 10 /xl may be chosen.

Potentiometric analysis at the microscale brings up special problems

and requires special precautions. The field of ion-selective microelectrodes has been reviewed by several workers [2 1 ,23].
294 ION-SELECTIVE ELECTRODES

A. POTENTIOMETRIC MEASUREMENTS In Vitro

Innumerable studies have been performed using macro and micro

ion-selective electrodes in vitro. Microelectrode analysis in vitro is ad- vantageous over other methods in that it does not require the measure- ment of a micro volume and its subsequent dilution, both of which are

potential sources of error. One potential source of error is the contamination of a small test sample by the leakage of salt bridge solution. This may

be minimized by using a conventional micropipette reference with a tip

diameter of less than 1 micrometer (/xm). However, the tip potential and

resistance of micropipettes with tips less than 1 in diameter may be

high.

The Radiometer thermostated pH capillary glass electrode reported by

Siggaard- Andersen [10] is widely used in biomedical laboratories for pH

measurement of biologic samples. The cell measures pH on a 25 ix\ sample of capillary blood with a standard deviation of ± 0.006 pH units. Intracellular protein extracts and desoxyribonucleic acids have been

studied for their cation binding properties in vitro using Na+ selective and

K+ selective glass electrodes. A variety of biologic solutions and tissues

have been studied with various types of ion-selective electrodes to measure ion species of physiologic or clinical interest. Innumerable potentiometric measurements were made on plasma and serum to determine

the ionic activities of H+, Na+, K+, Ca++, F" and I". Measurements have

been made on cerebrospinal fluid and urine for H+, Na+, K+, and Ca++

ionic activities. Gastric juice has been analyzed for H+, Ch and more

recently Ca++ ions. Recently, both saliva and mineralized tissues have

been studied with calcium and fluoride electrodes. The above-listed applications will be discussed individually in Section III. B. POTENTIOMETRIC MEASUREMENTS In VivO

Ion-selective electrodes have been adapted to biological measurements

in vivo on both a macro and a microscale. Perhaps the most unique ad- vantage of ion-selective electrodes is their capacity to monitor ion activities in vivo or in situ. Biological systems, even at the microscopic level, are quite complex

and heterogeneous. The geometry is usually not simple; the architecture

quite intricate. The colloidal polyelectrolytes and the enzymes of tissues

may occupy rather fixed sites. Our knowledge of the in situ intracellular ionic strength, osmotic pressure and the state of water itself is both scanty

and very uncertain. Without a reliable knowledge of the in situ pH, the

charge on the organic polyelectrolytes cannot be ascertained. Ion-binding

by the colloidal polyelectrolytes is pH dependent. The local in situ carbon

dioxide pressure is another element of uncertainty. The latter is one of the

factors that determine the local pH.
BIOMEDICAL RESEARCH 295

Although several uncertainties are involved in the in vitro determinations of ionic activities of biological systems in general, these uncertainties become even more serious in the case of pH measurement. This is due to the fact that a major biologic buffer has a gaseous component, i.e., CO2. The measurement of pH in situ is advantageous in that it eliminates

the uncertainty involved in the arbitrary choice of a CO2 pressure with

which to equilibrate the test samples. It also avoids the loss of CO2 to the

ambient air.

1. Extracellular Analyses

Friedman [24] has classified biologic systems into flowing and

non-flowing systems depending on whether or not the medium is static or

exhibits hydrodynamic flow. In extracellular potentiometric analyses of non-flowing biologic

systems, the shape of the indicator ion-selective electrode may be tailored to its mode of use in situ. For surface measurements, the electrode may

have a flat, convex or concave surface depending on the curvature of the

tissue under study. The spear shape is naturally suited for depth penetration. An important consideration in extracellular ion monitoring in situ is the response time of the ion-selective electrode. The electrode response

time should be short so that changes due to metabolic alterations may be

picked up promptly.

In situ monitoring of extracellular ionic activities has been applied to a number of non-flowing biologic systems. The ionic activities of H+, Na+,

K+, Ca++, CI- and F" have been measured wrth ion-sensitive electrodes.

Extracellular measurements in situ were performed in cerebrospinal fluid and on the brain surface, skeletal muscle, aqueous humor, the lumen of the stomach and gall bladder. In potentiometric analyses of flowing extracellular biologic systems,

the pioneering work was done by Friedman, et al. [1-2,24,25]. Although

it is elegant to monitor continuously the activity of various ions in a circulating fluid, the method should be carefully screened for artifacts arising

from streaming potentials and electrode response time. In this case the

streaming potential is the change in the electrode potential attributed to the flow of the electrolyte solution. Friedman, et al. [1] attributed the

changing streaming potential to a change in the composition of the liquid

junction of the salt bridge of the reference half-cell. They advise the maintenance of a constant flow rate to avoid these fluctuations. Friedman and

coworkers used flow-through or cannula electrodes of sodium and potassium glasses to measure the cationic activities in flowing arterial blood of

the rat [26] and the dog [27]. Rechnitz [28] has emphasized the critical importance of the electrode response time in ion monitoring in flowing

systems. Certainly the electrode response time must be fast enough and

should not itself be the rate-limiting step of the system.
296 ION-SELECTIVE ELECTRODES

In the nephrons of the kidney, the pre-urine flows through tubules of

microscopic caliber. Several authors [4,1 1,29-31] have measured the pH

or cation activities of the luminal fluid of single proximal tubules in situ. Figure 3 shows an indicator and a reference microelectrode localized

Figure 3. An indicator and a reference microelectrode in the lumen of proximal tubule.

within the lumen of a kidney tubule. Vieira and Malnic [31] used an an- timony microelectrode to measure the pH of tubular fluid in situ. The

other workers [11,29,30] used pH glass microelectrodes. Khuri, et at. [4], used microelectrodes of the Na+-sensitive glass N ASii-i« to measure Na+ activity in situ in the circulating blood, glomerular fluid and proximal tubular fluid of the Necturus kidney. The reference micropipette was

filled with 3M RbCl. The latter was selected as a salt bridge instead of the

usual KCl because of the extremely low sensitivity of Na-glass to Rb+

ion.

2. Intracellular Analyses

There has been a growing interest in intracellular ion analyses in situ with microelectrodes ever since the pioneering work of Caldwell [32,33].

Hinke [34,35] was the first to use sodium and potassium sensitive glass

microelectrodes to measure intracellular ionic activities. Following these

two investigators, there were several studies reported in which H+, Na+,

K+, C\- were measured in the protoplasm of single fibers of nerve, muscle

and the alga Nitella. Knowledge of intracellular ion activities is vital to our understanding of

many of the important phenomena in cellular physiology. The determina-
BIOMEDICAL RESEARCH 297

tion of intracellular ionic activity by means of an ion-selective microelectrode, if coupled with a separate determination of the total amount of the

ion species in question, could yield useful information about ion-binding

by the organic polyelectrolytes. Hinke and McLaughlin [36] found that,

whereas K was essentially free in the myoplasm, a significant part of in- tracellular Na is bound. Lev [37] found that 70% of the intracellular Na

content of the amphibian skeletal muscle is bound. In the squid axon, Hinke [35] concluded that 25% of the intracellular Na is bound whereas

the K is essentially free. The Na and K activity gradients across the membrane of the squid axon as determined by cation-selective glass microelectrodes by Hinke [35] are compatible with the generally accepted theory

of active and resting membrane potentials. Intracellular pH has been measured in different cells by several authors

using pH glass microelectrodes. Intracellular pH was measured by Caldwell [32,33] in crab muscle and the giant axon of the squid, by Kostyuk

and Sorokina [38] in frog sartorius muscle, by Lavallee [39] in cardiac

muscle, and Carter [40] in rat voluntary muscle. The intracellular pH observed ranged from 6.8-7.1, a value which is not compatible with a Donnan equilibrium distribution of H+ across cell membranes. The observed

values of intracellular pH by the above workers suggests that there is an

independent mechanism within the cells which regulates the intracellular

pH and maintains its stability at a level of H+ ion activity which is lower

than would be predicted from the Donnan equilibrium. But more recently.

Carter, et al. [41] have found an intracellular pH of 6.0 in the skeletal muscle of rats and they concluded that the H+ gradient across the cell membrane was in electrochemical equilibrium at all levels of the membrane potential.

There are a number of difficulties that plague intracellular analyses

using ion-selective microelectrodes. The first relates to the indicator

microelectrode and the major problem there is one of effective insulation

of all the probe except for the highly restricted sensitive tip. Paint insula- tion and glass insulation are the two major insulation techniques generally

used.

Technically, one has a choice between having two separate microelectrode half-cells or combining the ion-selective microelectrode and its reference into one physical unit. Having the cell as a single unit, although

technically more difficult, is advantageous in intracellular ion analyses.

The cell membrane is impaled at a single point and thus leakage is minimized. Also, the electrical potential difference across the cell membrane can be measured simultaneously and in the same cell whose in- tracellular ionic activity is being measured. Thus one can simultaneously

correlate trans-membrane ionic activity gradients with the trans-membrane electrical potential difference. The latter may be obtained by
298 ION-SELECTIVE ELECTRODES

recording the potential difference between an intracellular reference

half-cell and a similar half-cell located in the extracellular space. If the

potential of a cell is measured when the reference half-cell is in an extracellular location, one should subtract from the above the value of the

membrane potential in order to get the potential which is a measure of in- tracellular ion activity.

The Ling and Gerard [9] KCl-filled micropipette represents a miniaturized salt bridge component of the reference half-cell. A source of great

uncertainty is the liquid junction potential between the KCl-filled

micropipette tip and the intracellular medium. In the first place, our knowledge of intracellular ionic activities and ionic strength is quite scanty and uncertain. Secondly, the anionic intracellular polyelectrolytes may

selectively alter the ionic mobilities of the normally equitransferent KCl

bridge electrolyte. Thus the residual liquid junction potential, i.e., the dif- ference between its value in extracellular and intracellular media, is un- known and may well be significant. In the latter case, the magnitude of the

residual liquid junction potential is incorporated in the value of the in- tracellular ion activity or the membrane potential we measure.

ni. Biomedical Applications A. Glass Electrodes

Glass electrodes for hydrogen and other cations constitute a potent

analytical tool for cation analyses in biological systems. For an extensive

review of the subject the reader is advised to consult references

[21,22,24]. The pH function of some glasses was discovered quite early

in this century. But it was only a decade ago that Eisenman [42-44] began

his pioneering studies that resulted in the development of glass electrodes

sensitive to ions of the group la cation series. The special advantages of the glass membrane in direct potentiometric

analyses in living systems is that it is insensitive to oxidation-reduction

reactions, not greatly affected by proteins, and as such indifferent to anions in general. Glass is a highly workable material. Glass gradually

and continuously softens (decreasing viscosity) under progressive heating. This accounts for the easy workability of the glassy material into a wide variety of shapes, forms and sizes. Ion-sensitive glass membranes are anionic and function as cation

exchangers. The sensitive portion of the indicator glass electrode is nor- mally a continuous membrane bathed internally by a stable reference

solution. The external or measuring surface of the glass electrode is the

critical variable of the system whose cation exchange reactions with stan- dard and unknown solutions determine the change in the measured potential. The ion-sensitive glass membrane must be optimally hydrated to give
BIOMEDICAL RESEARCH 299

a Nernstian response. Dryness results in poor electrode function while

overhydration may dissolve a thin glass membrane. Glass electrodes may

undergo hysteresis when immersed successively in solutions of widely

varying composition. For that, it is advisable to frequently calibrate

ion-sensitive glass electrodes with standards that are not too dissimilar

from the unknown with respect to ionic strength, composition and pH

values.

Although the ion-sensitive membrane of the glass electrode must be a continuous and sealed structure, there has recently been several reports

of so-called incompletely sealed micropipette electrodes exhibiting ionic

selectivity and Nernstian response. Lavallee [39] found that open-tip

micropipettes (tip diameter < 1 fim) of Corning code 0150 glass had apH

sensitivity of about 30mV/pH unit when used against similarly filled Pyrex micropipettes. These cells yielded an intracellular pH of 6.9 in iso- lated rat atria. Lev [45] studied the electrochemical characteristics of the

incompletely sealed cation sensitive microelectrodes. He observed that irrespective of whether the glass is primarily Na+-sensitive or K+-sensitive, the resulting incompletely sealed micropipette is K+-sensitive. This

he attributed to a K+-selective anionic pore at the micropipette tip. These

microelectrodes were 8-9 times more selective to K+ as compared to Na+

ions and had a sensitivity of about 57 mV/pK unit. Ling [46] , by coating Corning code 0150 glass with collodion, obtained

electrodes of different selectivity orders depending on the manner in which collodion was treated. Gotoh, et al. [47] used a K+-selective col- lodion-coated glass to measure ion activity from the surface of the brain

in situ. Glass electrodes sensitive to the divalent cations Ca++ and Mg++ were

described by Garrels, et al. [48] but have not been applied, to our knowledge, in biomedical work. This is partly due to their not being sufficiently

selective to Ca++ over the other divalent cations (Mg+ + ) and the monovalent cations (Na+).

The three types of glass electrodes that have been used in biomedical

work are those for hydrogen (pH), sodium, and potassium ions.

/. Hydrogen Glass Electrodes

Among ion-selective glass electrodes, the pH glasses are sufficiently

selective to H+ ion relative to the other cations that they can be regarded

as pure and ideal electrodes. Both Na+ and K+ glass electrodes are essentially "mixed" electrodes. Measurements of pH in situ are to be preferred

whenever feasible. This will avoid CO2 loss to the ambient air. For mea- surement of pH in biological systems pH glass electrodes are favored over metallic or quinhydrone electrodes since the latter are sensitive to oxidation-reduction reactions and readily poisoned by proteins. For in

348-381 0-69—21
300 ION-SELECTIVE ELECTRODES

situ pH measurement, the probe must be made as small as possible since

tissue damage may increase the local acidity. Two general configurations

of pH glass electrodes are used: (1) the external probe (spear-shaped,

bulb), (2) the internal capillary. In the internal capillary configuration, the

sample or standard is taken up into the capillary lumen while the external

surface serves as the reference side. For pH determinations the internal

capillary geometry is preferred since the internal location of the sample

guards against gaseous (CO2) exchanges with the environment.

Dubuisson [49-5 1 ] used a flat membrane pH glass electrode in situ to monitor the extracellular pH changes during contraction and relaxation

of skeletal muscle. A ring device served to isolate only a film of extracellular fluid between the electrode membrane and the muscle surface. This

film was assumed to be in equilibrium with the underlying muscle. Following contraction pH changes, probably mediated by CO2 exchanges,

occurred in less than a second. These changes could be picked up since

the electrode response time was only a fraction of a second [51].

Sonnenschein, et al. [52] constructed and used spear-shaped pH elec- trodes for depth measurements of the pH of the brain in situ. More

recently, Meyer, et al. [53,54] introduced small pH probes into the brain

of cats and monkeys and monitored pH changes of the brain under

different metabolic conditions. Intracellular pH studies [32,33,38-41] were discussed in Section II-B-2. The kidney plays an important role in the acid-base balance of the living

organism. Normally, the kidney excretes the excess acids of metabolism

in order to regulate and maintain a constant pH in blood and other body

fluids. To study the renal handling of H + , it is important to measure the in vivo pH in single renal nephrons (see Fig. 3). Figure 4 shows a micropipette type of pH glass electrode (Corning

code 0150) which is insulated by mineral oil internally and by polystyrene

Ag-AgCl Polysterene

paint

10-20 pm

Cement

Figure 4. pH glass microelectrode with external insulation. paint externally. This indicator electrode was used against the reference

with the injecting mechanism (Fig. 2) in the manner represented by Figure

3 to measure the in vivo intraluminal pH in the proximal tubule of the rat
BIOMEDICAL RESEARCH 301

kidney [11]. A mean intraluminal pH of 7.22 ± 0.03 (standard error) was

obtained. Rector, et al. [30] using glaze-insulated pH glass microelectrodes found in the proximal tubule of the rat kidney a mean intraluminal

pH of6.82±0.13.

As mentioned earlier, the internal capillary configuration of glass elec- trodes has some distinct advantages particularly for pH determination.

Other factors which contribute to the superior electrode function of the

internal capillary configuration are the large area-to-volume ratio, the

small asymmetry potential and the probability that in the drawing process

the inner surface of a fine capillary is less subject to direct flame exposure

than the outer surface. Figure 5 shows an internal capillary pH microelectrode in combination

with the reference half-cell to form a single unit. This cell, developed by

Protecting 2'/o Agar

Calomel ! Wax glass (3MKCI)

pH 7

; butter Wax

Wax pH glass

Figure 5. Single unit pH glass ultra-microelectrode. Khuri, et al. [55], measures the pH of a sample of less than 0.05 /xl in volume and is particularly suited for in vivo applications [29]. In Figure

6 [56] the internal pH glass capillary (C-0150) was fused to a micropipette of an inert glass (C-0120) by means of a glass-to-glass seal. In view of their similar softening points and thermal expansion coeffi- cients, the ion-sensitive and insensitive glasses fuse readily. The electrode

shown in Figure 6 can measure the pH of samples of fluid as small as 0.01

/jlI in volume. The internal capillary pH microelectrodes shown in Figures

5 and 6 were used by Khuri, et al. [29] to measure the intraluminal pH at different points along the length of the proximal tubules of rat kidneys in vivo. The results revealed that the intraluminal pH falls as the tubular

fluid flows down the length of the proximal convoluted tubule. A signifi- cant inverse relationship was indicated by a correlation coefficient,

/?=-0.92.

To study the bicarbonate ion profile in the proximal tubule, Khuri, et al. [29] used the pH glass capillary microelectrode (Fig. 6) in the
302 ION-SELECTIVE ELECTRODES

Ag-AgCI

pH 7 buffer Glass-to- glass

seal

Protecting

glass

Glass-to-glass

seal

Glass

electrode

capillary C-0150

Micropipette C-0120

Bevelled

8 - 12

Figure 6. Glass ultra-microelectrodes, internal capillary type, glass-to-glass seal, measurement of pH.

Mm

for

gas-equilibration chamber (Fig. 7) to measure samples of tubular fluid in

vitro. The covering oil is equilibrated with a gas mixture having a known

percentage of CO2. At the time when the pH of an equilibrated sample of

tubular fluid is measured, the partial pressure of CO? {pCO-z) of the

equilibrated oil is determined by a Severinghaus CO2 electrode. From

these data one can readily calculate the bicarbonate concentration of tu3M KCl GAS DISPERSION TUBE

(Fritted glass) Ag-AgCl BUFFER

'

Figure 7. Lucite chamber for bicarbonate measurement of micro-samples with thermal and gas equilibrating mechanisms.
BIOMEDICAL RESEARCH 303

bular fluid. As with the pH studies, there was a definite tendency for the

bicarbonate concentration to fall as the fluid moved distally along the

length of the proximal tubule. The above illustrates that in dealing with a

solution whose major buffer is the bicarbonate-carbonic acid buffer, if the

CO2 pressure is known and constant, then pH glass electrodes could be

used in vitro to measure the bicarbonate ion concentration.

2. Sodium Glass Electrodes

The sodium alumino-silicate glass NASu-is of Eisenman [42] has been

widely used for making Na+-selective electrodes. The sodium electrode

glasses have the following selectivity order: Ag+ > H+ > Na+ >> K+, Li+,

--- >> Ca++. Although Na+-selective electrodes are mixed electrodes, in the neutral, high sodium, low potassium biological systems like plasma,

the electrode responds essentially to Na+. The NASn-is sodium glass has

selectivity ratios k^a-K ~ 0-005, /cnh-h —10. It is not sensitive to a change

in pH above a pH of 5.5. Still, it is a good practice to maintain a constant pH in the sodium standards with buffers. Gotoh, et al. [47] used Na+-sensitive electrodes (N ASu-is) to monitor

Na+ activity of the monkey's brain and blood in vivo simultaneously.

They observed changes in the extracellular Na+ activities of the brain

which correlated with changes of the metabolic activity of the cortex. Portnoy, et al. [57] carried out similar studies on the brain of the cat in

situ. Moore and Wilson [58] by determining sodium in human serum

with both sodium electrodes and flame photometry, found no evidence for

sodium binding in normal human serum. In a similar study of the state of

sodium in bile, Moore and Dietschy [59] concluded that sodium is bound

to the micelle structures. Sekelj and Goldbloom [60] applied Na glass

electrodes to the skin as a rapid screening and diagnostic test for cystic

fibrosis of the pancreas, a disease appearing at birth and characterized by

an elevated Na+ and C\- concentrations in sweat. In studies with Na+

glass microelectrodes, Hinke [35] concluded that 25% of the intracellular

Na of the squid axon is bound while Lev [37] found 70% of the intracellular Na of muscle to be bound.

The concentric cation glass microelectrode in Figure 8 was constructed

by Khuri, et al. [4,5] of either the Na+-glass NASh-ih or the K+-glass

KAS20-5. It is insulated internally with mineral oil and externally with

polystyrene. When it was used in vitro, as shown in Figure 9, only the sensitive area of the cation electrode was introduced into the aqueous

droplet. This afforded further external insulation of the shank by the

mineral oil of the Incite well. RbCl (3M) was used instead of the usual

KCl in the reference bridge because N ASh-ik glass is 100 times less sensitive to Rb+ than to K+ ions. Using the sodium cell of Figure 9 in vitro
304 ION-SELECTIVE ELECTRODES

Ag- A ri \nner Oi solution

' Polysterene

paint

^^^^f^^^mmm'

50-i00pm

i -

Y^^^r

'"^^

Cation glass Sensitive

Oil Pyrex Cement tip Figure 8. Concentric cation glass microelectrode with external insulation.

I

I Sample

Figure 9. Na+ microelectrode— RbCl (3M) cell (for Na+ measurement).

and in vivo as represented in Figure 3, the Na+ activity of serum, glomerular fluid, and proximal tubular fluid were essentially the same in Necturus

[4].

3. Potassium Glass Electrodes

The potassium-selective glasses like KAS2()-.^ and NAS27-4 are only 10

times more sensitive to K+ than to Na+ ions. The K+-glasses have the fol-
BIOMEDICAL RESEARCH 305

lowing selectivity order: > K+ > Na+ - -- >> Ca++. These are, therefore, truly "mixed" electrodes. In plasma the concentration ratio of

Na+/K+ is 35-40. Having at best a K:Na selectivity of 10:1, a separate

measurement of Na+ concentration is needed to obtain the K+ concentration. Therefore, using a Na-glass reference against the K-glass electrode

(see Fig. 1), Khuri, et al. [4,5] did not increase the steps involved in the potentiometric determination of K+. Besides the rationale for the use

of the K-Na all-glass cell presented in Section I- A, no salt bridge could be

identified to which the K-glass was sufficiently insensitive.

Using the all-glass cell (Fig. 1) and the sodium cell (Fig. 9) in succession, Khuri, et al. [4,5] measured K+ in proximal tubular fluid and plasma

in Necturus and the rat. A mean concentration ratio of potassium in tubular fluid/glomerular fluid of 1 .8 ± 0. 1 was obtained in Necturus. This contrasts with the mean potassium concentration ratio of tubular fluid/plasma

of 0.70 ± 0.03 obtained in the rat. K+-sensitive glass electrodes were used by Gotoh, et al. [47] and Port- noy, et al. [57] to monitor K+ activity of the brain of experimental

animals in vivo. Gotoh, et al. [47] used a collodion-coated C-0150 glass

after the design of Ling [46] to measure K+ activity. In intracellular applications of K+-sensitive microelectrodes. Lev [7]

and Hinke and McLaughlin [36] found that K+ is essentially free in the

myoplasm. Hinke [35] reached a similar conclusion in studies of the

squid axon. Figure 10 shows a cation sensitive electrode with the internal capillary

configuration. Microcapillaries of the sodium electrode glass NASn-is

fuse readily with Corning C-1720, whereas the potassium glass KAS20-5

fuses with C-0080. In Table 1, the soft point and the coefficient of thermal

expansion of the pH, sodium and potassium electrode glasses are tabulated along with those of the inactive glasses with which they readily fuse.

Reference Glass-to-glass Wax Wax Ag-AgCI solution

| seal

capillary

Figure 10. Glass ultra-microelectrode, interned capillary type, glass-to-giass seal.
306 ION-SELECTIVE ELECTRODES

Table 1. Some thermal properties of the electrode and "inert" glass

pairs that account for their readiness to fuse together.^

Glass Soft point Thermal expansion

°C 10-'^ in/in/°C

pH electrode: Corning 0150 655 110

Corning 0120 630 89

Na+ electrode: NASii_i8 > 970 53

Corning 1720 915 42

K+ electrode: KAS2o_5 '^96 102

Corning 0080 695 92

^ Tabulated values are quoted from Dr. N. C. Hebert, Corning Glass

Works, Corning, New York.

B. Non-Glass Electrodes

1. Metallic Electrodes

There are several subgroups of metallic electrodes:

a. A metal in contact with a solution having an ion of that metal. These

are referred to as electrodes of the "first kind" Hke Ag| Ag+ ( | designates

solid-solution interface).

b. A metal coated with a sparingly soluble salt of that metal. This has

been referred to as an electrode of the "second kind." An example of this group is Ag/Ag+Cl- (or Ag/AgCl) which is a Ch reversible electrode.

c. Metal amalgams like the amalgam electrodes for sodium and other

cations. In general, metal electrodes are poorly suited for potentiometric

analyses of biological systems. The metal ions may poison a living

system, and some biological constituents like proteins may poison metallic electrodes. Also, metallic electrodes are quite sensitive to the

oxidation-reduction reactions that are prevalent in living systems.

The silver-silver chloride (Ag/AgCl) electrode is reversible to chloride.

It is most widely used as a metallic internal reference element for the measuring and reference electrodes. Hansen, et al. [61] used Ag/AgCl elec- trodes to measure the chloride concentration in sweat by placing the elec-
BIOMEDICAL RESEARCH 307

trochemical cell on the skin surface. Infants suffering from cystic fibrosis had a higher Ch concentration in sweat than normal infants. Ag/AgCl

electrodes have been used to measure Ch in various biologic solutions.

Several workers have used Ag/AgCl electrodes to measure intracellular

Cl~ activity although it is known that protoplasm has constituents that are capable of reducing the silver ion. Also protein constituents may adsorb on the Ag/AgCl. Intracellular Ch was measured with Ag/AgCl

microelectrodes in the giant axon by Mauro [62] and Stockholm, et al. [63]. Hinke and McLaughlin [36], in an intracellular microelectrode

study of the barnacle muscle, concluded that a significant fraction of the

fiber's Cl~ and Na+ are bound to constituents of the myoplasm, as op- posed to the K+ ion which is free. The antimony electrode (antimony/antimony oxide) is a metallic elec- trode sensitive to H+ ion. Antimony electrodes were used to measure the

in situ pH of dental tissues by Thompson and Brudevald [64,65] . Kurella

and coworkers [66,67] used antimony microelectrodes to measure the in- tracellular pH of large plant cells. Recently, Vieira and Malnic [31] used

antimony microelectrodes to measure the intraluminal pH of proximal tu- bules of the rat kidney. However, in all these applications one should

keep in mind that antimony could be oxidized by oxygen, that antimony

oxide may be reduced by the protoplasmic reducing agents and that the

electrode may be poisoned by proteins.

2. Oxidation-Reduction Electrodes

The quinhydrone electrode represents this class. Its reaction involves

the reversible oxidation-reduction of the hydroquinone — quinone

system. It is of limited biological usefulness as an electrode for measuring

pH in view of its sensitivity to amino-acids, proteins and oxidation-reduction reactions. For about forty years the quinhydrone electrode has been

used in the measurement of pH of several biologic fluids [68,69]. In 1935, Pierce and Montgomery [70] described the technique of constructing micro-quinhydrone electrodes and used their electrodes to study

the site of acidification within the renal tubule of amphibia [71]. Several

renal physiologists [72,73] subsequently utilized micro-quinhydrone

electrodes to measure pH in vivo in single renal nephrons.

3. Ion-Exchange Membrane Electrodes

This represents a new class of ion-selective electrodes. A number of the

electrodes of this class are "mixed" electrodes with relatively low selectivity. The two major subgroups of this class are the solid-state and the

liquid membrane electrodes.
308 ION-SELECTIVE ELECTRODES

a. Solid-State Membranes. These are further subdivided into the

crystalline membrane electrodes and the precipitate-impregnated

(heterogeneous) membrane electrodes.

The crystalline membrane electrodes have a sensitive membrane sec- tioned from a single inorganic crystal of low solubility characteristics.

Electrodes sensitive to the halides F~, Cl~, Br", and I" have been

developed by Orion Research, Inc. Of this group, the fluoride electrode

of Frant and Ross [74] has received a great deal of interest in view of the

biologic and medical importance of fluoride. The sensitive portion of the

electrode is a small flat crystalline membrane. The fluoride electrode exhibits a Nernstian response over a wide range of fluoride activity. It is highly selective with a F iCh selectivity of more than 10^:1. Hydroxide

ion, the only interference, does not present a problem in the near-neutral

biologic systems. Fluoride ion activities have been determined with the

Orion fluoride electrode in serum, mineralized tissue, saliva and in pharmaceutical pastes, mouthwashes, and vitamins.

Durst and Taylor [75] modified the fluoride electrode for microchemical analysis. By using the crystalline fluoride-sensitive membrane as a cup

to contain the sample, the electrode was rendered capable of measuring

F" activity on samples as small as 1 0 yutl in volume.

Taves [76] made a comparative study, determining serum fluoride ion

concentration with the fluoride-electrode and with other methods. Concentration of the serum and isolation of the F" by diffusion was essential

since normal levels of serum F" are in the range where the electrode

response begins to be uncertain. He found the fluorescent method rather

superior to the colorimetric method. Because of the hysteresis that the

electrode exhibits when subjected to extremes in F" concentration over

a short span, Taves advises bracketing the unknown closely with stan- dards. In another study of serum fluoride utilizing the fluoride-electrode

and the morin-thorium reagent, Taves [77] obtained results which are consistent with the hypothesis that there are two forms of fluoride in human serum, an exchangeable and a non-exchangeable moeity.

Singer and Armstrong [78] determined fluoride in bone using the

fluoride electrode. The bone was ashed and the latter dissolved in an aqueous solution of constant pH and ionic strength. The mean fluoride content obtained by the electrode was in close agreement with the value

obtained by a chemical method. McCann [79] using the Orion electrode

determined fluoride activity in enamel, dentine, bone and apatite and

found the values to be in good agreement with the colorimetric method.

Gron, et al. [80] determined fluoride in human saliva with the fluoride

electrode. Since the electrode is almost equally sensitive to F~ and OH~,

it is advantageous to acidify the saliva. Using a recovery technique, Gron,

et al. found no evidence for F" complexes in saliva. Saliva was noted to

.
BIOMEDICAL RESEARCH 309

be a poor source of fluoride. They observed higher F" salivary values

after repeated ingestion of NaF. This was attributed to an overflow of F"

following the saturation of skeletal sites. Aasenden, et al. [81 ] studied the effect of oral topical treatments with

F- solutions on salivary fluoride. Following such treatment, salivary F~

was elevated for over a day. Following the routine use of fluoride-containing toothpaste, the salivary F" remained elevated for about 3 hours. The

decay characteristics of the increment in salivary F" can be described by

a simple exponential. The protracted elevation of salivary F~ after a topi- cal application was attributed to leaching of F" from the treated teeth. Shane and Miele [82] measured F~ in toothpastes with the fluoride

electrode. Toothpaste was converted into an aqueous mixture for the F"

determination. Fluoride ion was detected in toothpastes in the range of

0.22% as NaF and 0.40% as SnF-z. The precipitate-impregnated membrane electrodes consist of poorly

soluble inorganic salts precipitated in the matrix of an inert membrane.

The resulting membrane is a heterogeneous one, having a precipitate

phase and an inert phase. These electrodes are insensitive to oxidation-reduction reactions and not as vulnerable to protein poisioning

as the metallic electrodes. The precipitate-impregnated membrane elec- trodes currently available are selective for I", Br", and CI". Arino and

Kramer [83] used an iodide electrode consisting of a silicone rubber

membrane impregnated with Agl to measure the activity of iodide in iodinated proteins.

b. Liquid-Liquid Membrane Electrodes. The ion-exchanger in this group is in the liquid state. Being organic the liquid ion exchanger is hardly

miscible with water. The design that is currently being followed with

these electrodes is to hold the organic liquid ion exchanger within the

framework of a porous membrane. Using liquid anionic exchangers, elec- trodes selective to CI" and NO3 have been developed. However, it is the

Orion calcium electrode which occupies the position of prominence

among this group. The liquid ion exchange electrode with a favorable

Ca++ selectivity became available through the pioneering work of Ross

[84]. The calcium electrode is highly selective for Ca++ over Mg++. Its sensitivity for the group la monovalent cations is even lower than for Mg++. The only significant source of interference is H+ ion to which the

electrode is 10^ times more selective. For this reason alkalinization of the

solutions may be in order in some studies. The electrode response time is less than 30 seconds.

Perris and Whitfield [85] used the Orion calcium electrode to study the

influence of Ca++ activity on mitosis. They observed that mitotic activi- ty is affected by the level of ionized calcium in the cellular environment.
310 ION-SELECTIVE ELECTRODES

Woodward and Davidson [86] utilized a specific calcium electrode to study the Ca^^-binding ability of the protein polysaccharides of cartilage.

The stoichiometry of the binding process suggests that each calcium ion

is bound by two separate sulfate groups of the polysaccharide chains. The

protein polysaccharides of cartilage were found to chelate Ca^* ions very

effectively.

IV. References

[ 1] Friedman. S. M., Jamieson. J. D.. Nakashima. M.. and Friedman. C. L.. Science 130. 1252 (1959). Friedman, S. M..and Friedman. C. L.. Anat. Rec. 138. 129(1960).

Garrels, R. M., in Glass Electrodes for Hydrogen and Other Cations. G. Eisen man, Ed., Marcel Dekker, New York, 1967, pp. 344-361.

Khuri. R. N.. Goldstein, D. A., Maude. D. L.. Edmonds. C. and Solomon. A. K.. Amer. J. Physiol. 204, 743 (1963). Khuri, R. N.. Flanigan. W. J., and Oken. D. E..J. Appl. Physiol. 21. 1568 (1966). Lev, A. A.. Biophysica 9. 686 ( 1 964). Lev. A. A.. Nature 201. 1 132 (1964). Bates, R. G., Determination of pH: Theory and Practice, Chap. 3. John Wiley and

Sons, New York. 1964.

Ling, G. N., and Gerard. R. W.. J. Cell. Comp. Physiol. 34. 382( 1 949). Siggaard-Andersen, O., Scand. J. Clin. Lab. Invest.. Suppl. 15. 70 ( 1 963). Khuri, R. N., Rev. Sci. Instrum. 39. 730 ( 1 968). Grundfest. H..Kao.C. Y.. and Altamirano. M.. J. Gen. Physiol. 38. 245 ( 1 954). Semple.S. J. G..J. Appl. Physiol. 16.576(1961).

Khuri, R. N., Agulian, S. K. and Harik, R. I., Phys. Med. Biol. 13, 23 (1968). Khuri. R. N..and Merril.C. R.. Phys. Med. Biol. 9.541 (1964). Mueller, P., and Rudin, D. O., Biochem. Biophys. Res. Commun. 26. 398( 1 967). Ussing, H. H., J. Gen. Physiol. 43. 1 35 ( 1 960). Giebisch. G., J. Gen. Physiol. 44. 659 ( 1 96 1 ). Hodgkin, A. L..and Horowicz. P.. J. Physiol. 153.370(1960).

Hodgkin, A. L.,and Keynes. R. D..J. Physiol. 128.61 (1955). Hinke, J. A. M., in Glass Electrodes for Hydrogen and Other Cations. G. Eisen man, Ed.. Marcel Dekker. Inc.. New York. 1 967. pp. 464-477.

Khuri, R. N., in Glass Electrodes for Hydrogen and Other Cations, G. Eisenman

Ed.. Marcel Dekker. Inc.. New York. 1 967. ppp. 478-5 1 8. Lavallee, M., Schanne, O., and Hebert, N., Eds., Intracellular Glass Microelec

trodes, John Wiley and Sons, Inc., New York (in press-1969).

Friedman, S. M., in Glass Electrodes for Hydrogen and Other Cations, G. Eisen man, Ed., Marcel Dekker, Inc.. New York, 1967, p. 443. Friedman. S. M.. Meth. Biochem. Anal. 10,71 (1962). Friedman. S. M.. Jamieson. J. D.. Hinke, J. A. M.. and Friedman. C. L.. Proc. Soc.

Exptl. Biol. Med. 99. 727 ( 1 958). Friedman. S. M.. Jamieson. J. D.. Hinke. J. A. M.. and Friedman. C.L.. Amer. J. Physiol. 196. 1049(1959).

Rechnitz, G. A., in Glass Electrodes for Hydrogen and Other Cations. G. Eisen man, Ed., Marcel Dekker, Inc., New York. 1967. pp. 335-339.

Khuri, R. N.. and Agulian. S. K., Proc. Intl. Union Physiol. Sciences 7. 236 (1968). Rector, F. C, Carter, N. W.. and Seldin, D. W.. J. Clin. Invest. 44, 278 ( 1 965).
BIOMEDICAL RESEARCH 311

Vieira, F. L., and Malnic, G., Amer. J. Physiol. 214, 710(1 968). Caldwell, P. C, J. Physiol. 126, 169 (1954). Caldwell, P. C, J. Physiol. 142, 22 (1958). Hinke,J. A. M., Nature 184, 1257 (1959). Hinke,J. A. M.,J. Physiol. 156,314(1961).

Hinke, J. A. M., and McLaughlin, S. G. A., Can. J. Physiol. Pharm. 45, 655 (1967). Lev, A. A., Nature 201. 1 132 (1964). Kostyuk, P. G., and Sorokina, Z. A., Membrane Transport and Metabolism, A.

Kleinzeller and A. Kotyk, Eds., Academic Press, New York, 1961, pp. 193-203.

Lavallee, M., Circ. Res. 15, 185(1 964). Carter, N.W., Clin. Res. 9, 177(1961).

Carter, N. W., Rector, F. C, Campion, D. S., and Seldin, D. W., J. Clin. Invest. 46, 920(1967).

Eisenman, G., Rudin, D. O., and Casby, J. U., Science 126, 831(1 957). Eisenman,G., Biophys. J. 2,259 (1962). Eisenman, G., Advances in Analytical Chemistry and Instrumentation, Vol. 4, C. N. Reilley, Ed., Wiley-Interscience. New York, 1 965. Lev, A. A., in Intracellular Glass Microelectrodes, M. Lavallee, O. Schanne, and

N. Hebert, Eds., John Wiley and Sons, Inc., New York (in press- 1969). Ling,G. N.,J.Gen. Physiol. 43, 149(1960).

Gotoh, F., Tazaki, Y., Hamaguchi, K., and Meyer, J. S., J. Neurochem. 9, 81 (1962). Garrels, R. M., Sato, M., Thompson, M. E., Truesdell, A. H., Science 135, 1045

(1962). Dubuisson, M.,J. Physiol. 90, 47P ( 1 937). Dubuisson, M.,J. Physiol 94,461 (1939). Disteche, A., and Dubuisson, M., Rev. Sci. Instrum. 25, 869 (1954). Sonnenschein, R. R., Walker, R. M., and Stein, S. N., Rev. Sci. Instrum. 24, 702

(1953). Meyer, J. S., and Gotoh, F., Arch. Neurol. 3, 739 (1960). Meyer, J. S., Gotoh, F., and Tazaki, Y., J. Appl. Physiol. 16, 869 ( 1 96 1 ). Khuri, R. N., Agulian, S. K., Oelert, H., and Harik, R. I., Pflugers Archiv. 294, 291

(1967). Khuri, R. N., Agulian, S. K., and Harik, R. I., Pflugers Archiv. 301, 1 82 (1968). Portnoy, H. D., Thomas, L. M., and Gurdgian, E. S., Arch. Neurol. 8. 597 (1963). Moore, E. W., and Wilson, D. W., J. Clin. Invest. 42, 293 (1963). Moore, E. W.,and Dietschy,J. M., Amer. J. Physiol.206, 1111 (1964).

Sekelj, P., and Goldbloom, R. B., in Glass Electrodes for Hydrogen and Other Cations, G. Eisenman, Ed., Marcel Dekker, New York, 1968, pp. 540-553. Hansen, L., Buechele, M., Koroshec, J., and Warwick, W. J., Amer. J. Clin. Path. 49, 834(1968).

Mauro, A., Fed. Proc. 13,96(1954).

Strickholm, A., and Wallin, B. G., Nature 208, 790 (1965). Thompson, F. C.,and Brudevold, F.,J. Dent. Res. 33, 849 ( 1 954). Brudevald, F., and Thompson, F. C, J. Dent. Res. 33, 854( 1 954). Kurella,G. A., and Popov, G. A., Biofizika (Russian) 5, 373 ( 1 960). Vorobiev, L. N., Kurella, G. A., and Popov, G. A., Biofizika (Russian) 6, 581

(1961). Lang, E. P., J. Biol. Chem. 88, 55 1 (1930).

Pierce,.). A., J. Biol. Chem. 111,501 (1935).

Pierce, J. A., and Montgomery. H.,J. Biol. Chem. 110,763 (1935). Montgomery, H., and Pierce, J. A., Amer. J. Physiol. 118, 144 (1937).
2 ION-SELECTIVE ELECTRODES

Gottschalk, C. W., Lassiter, W. E., and Mvlle, M., Amer. J. Physiol. 198,581 (1960). ClappJ. R., Watson, J. F.,and Berliner, R. W., Amer. J. Physiol. 205, 693 (1963). Frant, M.S., and Ross, J. W., Science 154, 1553(1 966). Durst, R. A., and Taylor, J. K., Anal. Chem. 39, 1483 (1967). Taves, D. R., Talanta 15, 1015 (1968). Taves, D. R., Nature 217, 1 050 ( 1 968). Singer, L. , and Armstrong, W. D., Anal. Chem. 40, 6 1 3 ( 1 968). McCann, H. G., Arch. Oral Biol. 13, 475 (1968). Gron, P., McCann, H. G., and Brudevold, P., Arch. Oral Biol. 13, 203 (1968). Aasenden, R., Brudevold, P., and Richardson, B., Arch. Oral Biol. 13, 203 ( 1 968). Shane, N., and Miele, D., J. Pharm. Sci. 57, 1260 (1968). Arino,H., and Kramer, H. H.,Nucl. Applic. 4, 356 ( 1 958). Ross, J. W., Science 156, 1378 (1967).

Perris, A. D., and Whitfield, J. P., Nature 216, 1350(1967).

Woodward, C, and Davidson, E. A., Biochem. 60, 20 1 (1968).
CHAPTER 9

ANALYTICAL STUDIES ON

ION-SELECTIVE MEMBRANE ELECTRODES

Garry A. Rechnitz

Department of Chemistry

State University of New York

Buffalo, New York 14214

I. Introduction

The development and continuing improvement of ion-selective membrane electrodes during the last few years has been of particular benefit to analytical chemistry [ 1 ] . From the analytical viewpoint such electrodes

are nearly ideal measurement tools because of their ability to selectively

monitor the activity of certain ions in solution both continuously and nondestructively. It is not surprising, therefore, that a large number of

analytical applications of the electrodes have already been developed.

To focus attention only upon the direct analytical applications of

ion-selective electrodes would be a disservice both to the scope of the

electrodes and the catholic interests of modern analytical chemists, however. The range of what can be called "analytical studies" using ion-selective electrodes as measurement devices and of the electrodes themselves

has been very wide indeed. This review is an attempt to communicate

something of this range by a description of relevant studies involving the use of electrodes in equilibrium and kinetic solution chemistry as well as of the interesting and challenging problems raised regarding the method

of operation of ion-selective membrane electrodes; the latter also illus- trates the interplay between application needs and fundamental investigation which is so necessary to the further development of new electrode

systems.

11. Principles

While I have been specifically asked to emphasize the newer kinds of

membrane electrodes in preference to glass electrodes, it must nevertheless be recognized that much of our present understanding arises from

basic studies performed on glass electrodes and that much of our reasoning concerning ion-selective electrodes is by analogy to glass electrodes.

The continuum of cation-selective glass electrodes is now known to be- long to the 'Tixed-site" category [2] of ion-exchange membrane elec- trodes. This simply means that the active sites on the surface or in the

313
314 ION-SELECTIVE ELECTRODES

hydrated layer of the glass are not free to move about during the time

scale of the measurement. It is further recognized that the electrode

potential arises from a combination of cation exchange and cation mobility factors. The quantitative physical meaning of the observed selectivity

ratio of such electrodes is, in fact, the product of the ion-exchange

equilibrium constant between the sites and the solution and the mobility

ratio of the exchanging ions in the hydrated layer of the glass. Thus, the

selectivity properties of a desired electrode can be produced by ap- propriate adjustment of these parameters through alteration of the glass

composition or by appropriate surface treatment. This simple model

ought to be applicable to fixed-site types of electrode membranes, in general, and is indeed useful in the study of solid matrix or crystalline

membrane electrodes.

These considerations are also useful in the treatment of liquid membrane electrodes with the added complication that the "sites" are also free

to move in the active phase of these electrodes. This is an important ad- vantage from the point of view of practical electrodes because it makes

possible the design of electrodes having appreciable selectivity for multivalent ions over univalent ions. Because the potential of ion-selective electrodes is actually composed

of two or more discrete contributions arising from the various processes

at the interfaces and in the bulk of the active membrane material, it fol- lows that these several components can be separately discerned under

certain experimental conditions. This is particularly true when such elec- trodes are used under non-steady state conditions, say in flowing samples

or in changing reaction systems. The resulting behavior can have signifi- cant consequences to the interpretation of experimental measurements

carried out under dynamic conditions.

Specifically, when the potential of an ion-selective electrode is monitored as a function of time in a system of rapidly changing composition,

the potential determining processes at and in the electrode membrane

may also be rate determining and result in various "transient"

phenomena.

This effect has recently been demonstrated for cation-sensitive glass

electrodes [3] . When such electrodes are subjected to a sudden change in activity of divalent cations such as Ca++ or Sr++ in the presence of a constant background concentration of univalent cations, the electrode potential undergoes a momentary (<100 msec) excursion far beyond that pre- dicted by the equilibrium selectivity of the electrode for the ions involved

(Fig. 1). At slightly longer times, the potential returns to the expected

value. This behavior, while initially puzzling, can now be explained on the

basis of the above mentioned two components which make up the potentiometric selectivity of the electrode, i.e., the ion-exchange equilibrium
ANALYTICAL STUDIES 315

Figure 1. Transient response to divalent cations of cation-sensitive glass electrodes. K+

background= lo w, pH = 9. A) 0.0538M Ca+ + ^0.0100M Ca++. B) 0.0538yv/ Sr+ + ^O.OIOOM Sr++.
316 ION-SELECTIVE ELECTRODES

constant and the mobility ratio. In the experimental system illustrated in Figure 1, we have a situation where the ion-exchange equilibrium

between Ca++ or Sr++ and K+ substantially favors the up-take of the

divalent ion by the electrode. This effect is momentarily dominant when

the activity of the divalent ion is changed near the electrode surface and

gives rise to the initial excursion of the potential. The mobility of divalent

ions in the hydrated layer is vastly lower than that of univalent cations in the hydrated layer of the glass; thus, the mobility ratio factor more than

cancels the favorable ion-exchange equilibrium constant and causes the

potential to return to the final steady-state value when both factors are in

full effect. Ordinarily, such phenomena would not be noticeable in experiments car- ried out with. ion-selective electrodes on the normal laboratory time scale. In the study of fast reactions, to be described below, these effects can

pose a practical limitation to accurate experimentation, however. More

seriously, similar effects are also observed on liquid membrane electrodes

where the time scale of electrode response is very much expanded (Fig.

2). As a result, the effective use of such electrodes for rate studies is dif- ficult even for moderately rapid reactions under certain circumstances.

I mV

10 sec

Figure 2. Transient Mg2+ response of Ca^^-selective liquid membrane electrode. pH = 9.63; /=0.01M 25°C. (a)[Mg++] = 0-^ 2.5 x IQ-W; [Ca++] = 3.9 x IQ-W. (b) [Mg++] = 2.5X 10-W-^4.9x IQ-W; [Ca++J = 3.7x IQ-W.

Because the equilibrium selectivity of liquid membrane electrodes having

"mobile" sites involves at least three separate components [2], the observed transient effects cannot yet be unambiguously interpreted.
ANALYTICAL STUDIES 317

Another common and, as yet, unexplained phenomenon is the "slowing" of electrode response in the presence of interfering ions. The sodium

selective glass electrode, for example, shows (Fig. 3) a more sluggish

response to changes in Na+ activity in the presence of K+ ions than in their absence. Similarly, the calcium selective liquid membrane electrode

responds more slowly to changes in Ca++ activity when magnesium ions

are present than when they are not (Fig. 4). A systematic investigation of

these effects is currently underway but, in the meantime, it must be recog- nized that this slowing of response rates could be a source of error in the

investigation of practical systems under dynamic conditions.

Equilibrium selectivity considerations, alone, present one of the limit- ing factors in the use of ion-selective electrodes for analytical studies. In

this connection, it is convenient to speak in terms of accessibility "windows" for each electrode in a given system. For the LaFs crystal, fluoride

selective electrode, for example, there is an accessibility window with the

solution pH as the variable because the usefulness of this electrode is limited by OH~ interference at high pH values and by the formation of

hydrogen fluoride species at low pH's. Similarly, the liquid membrane

cupric ion-selective electrode has a pH window defined by its response to the hydrogen ion in acidic media and by the formation of cupric hydroxide

in more alkaline media.

Such accessibility windows may be enormously large, as in the case of

the pH type glass electrode, or distressingly narrow, as is the case for some of the recently developed liquid membrane electrodes. Naturally,

the solution pH is not the only determining variable in the definition of

those windows. Any interfering ion, "poisoning" material, or physical

variable has an effect which can be expressed in terms of such windows

for any given electrode. It has been my experience that most of the

problems encountered by users, especially new users, of ion-selective

electrodes can be traced to a lack of appreciation of this concept, the

violation of some simple rule regarding electrode treatment and handling, or confusion about the elementary activity relationships used for the in- terpretation of potentiometric data. It should not be necessary to do

this but it must be stated again: ion-selective electrodes measure

activity — not concentration

!

III. Complexes

An especially attractive consequence of the fact that ion-selective elec- trodes measure the activity of unassociated ions is that such electrodes can be used directly and elegantly in the study of complexes and other as- sociated chemical species. In principle, all that is necessary is to measure

the activity of the ion of interest under noncomplexing solution conditions
318 ION-SELECTIVE ELECTRODES

V.,^ c

I

\ \ \ \

1 0 2 4 6 8 10 seconds

Figure 3. Effect of K+ background upon dynamic response of Na+-selective glass elec- trode to change in Na^ concentration from 0.0538/^ Na+ to 0.01 OOM Na+. back- ground (a) O.IOOOM; (b) 0.0500M; (c) 0.0.
ANALYTICAL STUDIES 319

b

I mv

Figure 4. Slowing effect of Mg-+ on response rate of Ca^^-selective liquid membrane

electrode. pH = 9.63; / = 0.01M; 25 °C. [Ca++J= l.Ox IQ-W^ 1.33 x IQ-W. (a) 3x 10-W Mg++. (b) no Mg++.

and then again in the presence of the complexing agent. From these measurements and knowledge of the initial concentrations of the reagents in- volved, both the stoichiometry and the formation constant of the resulting

complex can be obtained by standard methods. Situations involving series of complexes, additional equilibria, kinetic complications, etc., can also

be handled through proper design of experiments and use of appropriate

computational techniques.

Practically every category of ion-selective electrodes has, by now, been

employed for complex formation studies. The species involved have

ranged from simple inorganic ion pairs to large complexes of biological in- terest. The fluoride sensitive membrane electrode is, because of its large

accessibility window, a particularly convenient device for the purpose of

studying fluoride complexes. It also has the desirable property of time sta- bility as is demonstrated in Figure 5 where two calibration curves obtained with the same electrode but with a two-month time interval are dis- played. Both calibration curves have the theoretical slope.

As already mentioned, the accessibility window of the fluoride elec- trode is limited in acidic solutions by the tendency of the fluoride ion to form hydrogen fluoride species. It should, therefore, be possible to study

the formation of such species using the electrode to monitor the decreasing activity of free fluoride ion as the acidity of the medium is increased.

Incidentally, if the results agree well with independent studies we should

also have a confirmation of the hypothesis that the electrode indeed is only responsive to uncomplexed fluoride.
320 ION-SELECTIVE ELECTRODES
ANALYTICAL STUDIES 321

The equilibria

H + + F-^ HF (1)

and

HF + F-^HF7 (2)

should be dominant in acidic, aqueous solutions of fluoride. With this model in mind, it is then appropriate to carry out simultaneous determinations of H+ and F", using the pH type glass electrode and the LaFs crystal

electrode, respectively, on a series of solutions of systematically varying

composition, but of constant ionic strength and temperature. The results [4] of such a series of measurements are shown in Table 1 which gives n,

the average number of fluoride ions bound per hydrogen ion, over a wide

range of conditions. These data can then be converted into a Bjerrum plot

(Fig. 6) which indeed shows two "breaks" indicative of the formation of

1.8 r

n

Log [F-J Figure 6. Bjerrum plot for H+-F~ interaction in aqueous solution. Data taken with F -selective electrode.
322 ION-SELECTIVE ELECTRODES

Table 1. Free fluoride concentration and average number of fluoride ions

bound per hydrogen ion at different total fluoride and acid

concentrations. LF Jt IH Jt -log[F ] n 0.0040 0.1500 4.430 0.026

0.0040 0.1162 4.347 0.034

0.0080 0. 1500 4.222 0.053

0.0040 0.0581 4.066 0.067

0.0080 0.1162 4.061 0.068

0.0040 0.0291 3 7*^5 0 131 0.0200 0. 1500 O3 68*^ . vJOO 0 132

0.0400 0. 1500 O.3 OO'^'^li 0 264

0.0010 0 0020 0 26t

0.0040 0 01 162 3 2Q8 0 301 0.0010 0.0010 3 176 0 333

0.0600 0.1500 3 071 0 304

0.0080 0 001162 2.934 0.471

0.0800 0. 1500 2.863 0 524

0.0080 0.01162 2.810 0. 555

0.0400 0.05809 2.660 0.651

0.1000 0. 1500 2.648 0.652

0.0100 0.01162 2.652 0.669

0.0040 0.001162 2.498 0.708

0.0080 0 005809 2.442 0.755

0.0400 2 348 0 81

T

0.0100 0.005809 2.298 0.855

0.0400 0.02905 1.943 0.985

0.0200 0.005809 1.848 0.998

0.1000 0.0581 1.463 1.129

0.2981 0.2033 1.331 1.237

0.3974 0.2033 0.939 1.389

0.4968 0.2324 0.799 1.454

0.5347 0.2558 0.837 1.522

HP and HF2 , respectively. The experimental results may also be quantitatively evaluated in terms of the equilibrium constants for Equations (1) and (2); the results of this evaluation are given in Table 2 yielding mean

values of lO^-^o and lO^-^^ for Kx and Ki, respectively. Since these values

are in excellent agreement with prior studies, our hypothesis regarding the

response of the electrode can be considered as confirmed.

With this knowledge of the properties of the LaFa electrode and the in- formation about fluoride equilibria in acidic media, the electrode can then
ANALYTICAL STUDIES 323

Table 2. Formation constants of HF and HF2 calculated for each

experimental set of[F~l and n.[HF] [UFJ 1 K, = ; K., . [H+][F-] [HF][F-]

n L r J log K 1 log A2

0.131 0.0001842 2.91 0.72

0.132 0.0002075 2.86 0.77

0.264 0.0004666 2.88 0.75

0.265 0.0004700 2.88 0.75

0.301 0.0005035 2.93 0.71

0..333 0.0006670 2.87 0.77

0.394 0.0008491 2.88 0.76

0.471 0.001165 2.87 0.76

0.524 0.001371 2.89 0.74

0,555 0.001548 2.89 0.74

0.651 0.002188 2.91 0.73

0.652 0.002249 2.90 0.74

0.669 0.002229 2.94 0.70

0.708 0.003176 2.85 0.79

0.755 0.003617 2.89 0.75

0.815 0.004488 2.93 0.70

0,855 0.005035 2.97 0.81

0.985 0.01140 2.93 0.87

0.998 0.01419 2.89 0.80

1.129 0.03443 2.88 0.76

1.237 0.04662 2.88 0.88

1.389 0.1151 2.88 0.76

1.454 0. 1589 2.91 . 0.73

1.522 0. 1455 2.89 0.89

Mean value 2.90 ± 0.03 0.77 ± 0.05

be employed with confidence for more challenging complex formation

studies. Of particular interest and practical importance is the interaction

of fluoride with heavy metal ions, which is difficult to monitor directly

with other techniques. Some representative data for the formation of

iron(III) complexes of F~, using the techniques described above, are given in Table 3. Here 7i is defined as the average number of F~ bound

per Fe^+, and it is clear that the predominant species under these conditions are FeF-+ and FeF.J^. At higher fluoride concentrations it is also
324 ION-SELECTIVE ELECTRODES

Table 3. Average number of fluoride ions bound per ferric ion at different

concentrations of free fluoride ion.

[F-] X 10^ M n [H+1 M n h + A. \

V [H-] /

0.06731 0.07215 0.1316 0.07306

0.06702 0.07235 0.1316 0.07326

0.08919 0.08557 0.06887 0.08763

0.1129 0.09513 0.03722 0.09938

0.1005 0.1050 0.1316 0. 1063

0.1443 0.1367 0.06646 0.1401

0.1393 . 0.1412 0.1316 0. 1430

0.2094 0.1633 0.03359 0.1714

0. 1862 0.1684 0.06887 0.1724

0.2379 0.1880 0.03722 0.1964

0,2057 0.2040 0.1316 0.2065

0.3146 0.2621 0.06645 0.2686

0.3035 0.2657 0.1316 0.2690

0.2987 0.2689 0.1316 0.2723

0.4453 0.3179 0.03359 0.3336

0.4128 0.3225 0.06887 0.3303

0.3887 0.3259 0.1316 0.3299

0.4479 0.3612 0.1316 0.3657

0.5458 0.3624 0.03722 0.3785

0.5517 0.3906 0.06887 0.4000

0.7366 0.4425 0.03722 0.4622

0.5662 0.4434 0.1316 0.4490

0.7187 0.4657 0.06646 0.4773

0.9421 0.5535 0.06646 0.5673

1.115 0.5604 0.03359 0.5878

1.528 0.6552 0.03359 0.6875

possible to form the species FeFs, FeFj , FeF|", FeFg" and to evaluate

their formation constants; such a quantitative study is currently in progress. Further relevant details [5] with regard to fluoride complexes are also given below in connection with the formation kinetics of

the monofluoroaluminum(III) complex.

The crystalline Ag2S membrane electrode, which is sensitive to the sul- fide ion, is also well suited for complex formation studies because of its remarkable lack of interferences. Unfortunately, the chemistry of sulfide ion in aqueous solution is complicated by the tendency of that ion to in- teract with the solvent to form US' and H2S species to which the elec- trode is not responsive. This tendency is illustrated in Figure 7 where the
PH

Figure 7. Response of Orion S= electrode to S= as function of pH, at 7 = 0. IM. A =

5x 10-W Na2S; B= 1 x IQ-W Na-.S; C = 2x IQ-W Na2S. decreasing response of the electrode with decreasing pH values at other- wise constant conditions is clearly visible. Because of this effect, the elec- trode has its optimum sensitivity in alkaline media [6]

.

In such media, however, the electrode is admirably suited to the study

of sulfide complexes. The formation of the thiostannate complex ion, for

example, proceeds according to SnS2(i')+S--^SnS;i- (3)

and can be very precisely evaluated by simultaneous measurements with

the pH type and sulfide ion-selective electrodes. Some relevant results are shown in Table 4. The average value for Kj, 2.062 x 10\ agrees very

well with a previously reported value of 1. 1 x 10\ obtained under slightly

different solution conditions. Because the electrode gives a direct measure of the sulfide activity, the present value has an uncertainty of

only ±5% and is probably quite accurate, as well.
326 ION-SELECTIVE ELECTRODES

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ANALYTICAL STUDIES 327

While liquid membrane electrodes require somewhat greater skill and

care for reliable use in fundamental studies, they are also excellent and

useful tools for complex formation studies. As a general statement, it can be said of liquid membrane electrodes that they have more restricted ac- cessibility windows than either glass or crystal membrane electrodes.

This is a direct consequence of the fact that liquid membrane electrodes

are more prone to potentiometric interference from both cations and

anions. On the other hand, the liquid membrane electrodes are responsive

exactly to those ions, e.g., Ca+ + , ClOj, NO3 , BF4 , etc., which are extremely difficult to monitor by other techniques. Thus any extra effort required in the handling of the electrodes and the selection of optimum

conditions is well repaid by the possibility of studying previously inac- cessible systems.

The cupric ion-selective electrode, for example, responds selectively to Cu++ over the 10-- to lO^-^ molar range in the pH region of 3.5 to 6.5. Thus, the electrode can be used to study soluble copper complexes in- volving ligands of appropriate acid-base properties. The results of such a study are summarized in Table 5 where the complexing ligands have been

chosen, in part, because of their biological significance. The results agree

well with available literature data, and the method, using the direct measurement of Cu++ activities, is thought to be superior to alternate methods

Table 5. Formation constants of copper (II) complexes determined with

the cupric ion— selective electrode (at 25 °C and / = 0. lAI).

Ligand pH Kf{^(measured) Kyditeratiu-e)

Glycine 6.06 ^1 ^= 10^ 20

(/ = 0.01.\I)

_ ^ol4.96

6.00 ^'1 . 10^ 36

(/ = O.IM)

Glutamic Acid 6.00 ^'1 ^= 10^ 48 ^2 ^

THAM'' 6.00 ^'1 ^= 10^ 97

Acetate 5.75 ^1 ^= 10^ 04

(/ = O.I AI. 25 °C) ~ 10^ K2 -10^^

(/ = l.OM, 20 °C)

Tr /,s [hydroxymethyl] aminomethane
328 ION-SELECTIVE ELECTRODES

(such as pH titration) because of its simplicity and potential applicability

to a wide range of ionic media.

Because of the difficulty of measuring free calcium activity by conventional analytical methods, the use of the Ca++ selective membrane elec- trodes of the liquid membrane type is particularly attractive in the study

of calcium complexes. For such studies, we [8] made use of the equation

£ = £"+0.0295 log +

where y and [ ] signify activity coefficients and analytical concentrations

while jSj and [L]j are the overall formation constants and ligand concentrations, respectively, of any ligand which complexes Ca2+. Ki and denote

the selectivity ratios and charges of any interfering cations which may be

present; fortunately the electrode is sufficiently selective for Ca2+ so that the second term in Equation (4) can be minimized.

The chelating agents ethylenediaminetetraacetic acid (EDTA) and

nitrilotriacetic acid (NTA) were studied in detail and their interaction

with Ca2+ is graphically presented in Figure 8, as a function of pH, in terms of a "titration" of a constant amount of Ca-+ by increasing quantities

of ligand. The resulting curves can be mathematically analyzed to yield

the quantitative overall formation constants shown in Tables 6 and 7 for EDTA and NTA, respectively. Formation constant values obtained at other pH's were as follows: for Ca(II)-NTA, 1.32 x 10-^ (pH = 7.8-8.1), 3.2 X 10-^ (pH = 8.4-8.5) and for Ca(II)-EDTA, 8.80 x 10-^ (pH = 5.26).

These results are in good agreement with reported literature values. These studies were extended to some biologically important Ca2+ complexes using the interesting new Beckman 39608 Ca2+ selective electrode

which utilizes a solid matrix ion exchanger and, thus, has somewhat dif- ferent selectivity characteristics than the Orion or Corning liquid membrane electrodes. The results for calcium malate, citrate, and DCTA

{trans- 1 ,2-diaminocyclohexane-N ,N ,N ' ,N ' -tetraacetic acid) complexes

are given in Tables 8-10; once again the formation constants obtained are

in good agreement with the literature values shown at the foot of each

table.

It should not be thought that the general method described is restricted

to cation selective liquid membrane electrodes. Indeed, the recent development of electrodes for CI", NO3 , CIO4 , BF4, etc., has opened

a whole new field of investigation involving the association of these

anions with other ions. This possibility is particularly attractive because

of the lack of independent techniques for the selective and direct measure- ment of the activity of these ions. A relevant illustration is provided by our recent studies involving the

perchlorate electrode [9]. This electrode has a useful response to CIO4
ANALYTICAL STUDIES 329

I I

I \ \ I \ I L I I 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 ml titront

Figure 8. Titration curves monitored with Ca-+-selective electrode. 77 ml of 3.573 x 10-W Ca2+ with 0.02M TEA-NTA or TEA-EDTA iI = 0.0\M, TEA-borate media,

25 °C).

in the 10-^ to lO-^-^ molar range in aqueous systems of pH 4 to 11, and

has reasonable selectivity for C104^ over common anions such as ni- trate, bicarbonate, and the halides. The response of the electrode to CIO4 activity is illustrated by Figure 9 as a function of temperature,

and the results of some solubility determinations, obtained by measuring
330 ION-SELECTIVE ELECTRODES

Table 6. Titration data of 77.0 ml of 3.573 x 10~^ M Ca^+ with 0.0200 M

TEA-EDTA, / = 0.01, pH = 4.75, TEA-acetate.

EDTA [EDTA]^ [CaYle K

' mlml X iU ivl X lU M X lU M X 10 M X 10 M X 10 M

^

0.40 3.553 1.034 2.67o 0.883 1.5i 2.19^

0.60 3.544 1.546 2.346 l.llg 4.28 1.12^

0.80 3.535 2.056 2.02o 1.515 5.4i 1.39^

LOO 3.5:^ 2.564 1.78o 1.746 8.18 1.20 1.20 3,5l6 3.O69 1.53o 1.986 10.83 1.20 1.30 3.5I2 3.32i 1.43o 2.O82 12.39 1.18 1.35 3.5O9 3.446 1.38o 2.129 13. 17 1.17 1.40 3.508 3.572 1.33o 2.178 13.94 1.18 1.50 3.5O3 3.822 1.25o 2.253 15.69 1.15 1.60 3.499 4.07i 1-165 2.334 17.37 1.15 mean 1.18 X 10^

[ total concentration, [ ]^ : equilibrium concentration,

{L\qI : total ligand species concentration at equilibrium,

^ : not included in average; K ' = [CaY]e/(Ca^+)e (L)^^

the activity of free CIO4 in equilibrium with the relevant precipitate, are shown in Table 11.

It certainly seems that the general utility of ion-selective electrodes for complex formation and other ion association studies has already been

demonstrated and that a widespread use of electrodes for such measure- ments can be expected in the future. IV. Kinetics

Since ion-selective membrane electrodes are capable of monitoring

changes in ion activities continuously and with generally good dynamic

response, one of the more fruitful areas of application of electrodes ought

to be in chemical and biochemical kinetics. We have, thus, been trying to demonstrate the usefulness of ion electrodes for reaction rate measure- ments and mechanistic investigations through the study of a number of
ANALYTICAL STUDIES 331

Table?. Titrationdataof 77.0 ml of 3.57 x lO'^^M Ca^^ with 0.0200 M

TEA-NTA,/ = 0.01, pH = 7.3 - 7.6, TEA-borate.

NTA [Ca+2]^ [NTA]^ [CaYle met K

' ml X lU^M X lU^ M X 10^ M X 10^ M X 10^ M X 10 ^ M ^

0.40 3.553 1.034 2.7^ 0.883 2.O1 1.52^

0o60 3.544 1.546 2.265 1.279 2.&7 2.12a

0.70 3.54o I.8O2 2.060 1.48o 3.22 2.23a

0„80 3.535 2.056 l:84o 1.695 3,61 2.55a

0.90 3.53o 2.3I0 1.62o 1.9 Ifl 4.O0 2.95a

1,00 3.526 2.564 1.445 2.O81 4.83 2.98

1.10 3.52i 2.8I7 1.292 2.229 5.88 2.93

1.20 3.51^ 3.O69 1.15o 2.366 7.O3 2„93

1.30 3.5I2 3.32i 1.035 2.477 8.44 2.84

1.40 3.508 3.572 0.906 2.592 9.80 2.92

1.50 3.5O3 3.822 0.795 2.708 11. 14 3.06

1.60 3.499 4.07i 0.697 2.8O2 12.69 3.17 a mean 2.94 X 104

[ ]^ : total concentration, [ ]^ : equilibrium concentration

,

[y^f • total ligand species concentration at equilibrium,

a

: not included in average; K ' = [CaY]e/(Ca2+)^ (L)^^

model systems. It will be seen below that this effort has been largely successful. Our work in this area began with the application of cation-sensitive

glass electrodes to the study of heterogeneous reactions involving the

precipitation of various alkali metal ions with tetraphenylboron [10].

This early work is important because it demonstrated that even rather fast reactions (rate constants in the 10^ range) could be studied with elec- trodes whose response times (see above) might ordinarily be considered

rate limiting. The method used to overcome this limitation is, of course,

the steady-state approach; specifically, the reactants are rapidly mixed in a continuous flow system and streamed past the sensing electrode at a

controlled rate. The electrode "sees" only a constant environment and,
332 ION-SELECTIVE ELECTRODES

Table 8„ Formation constants of Ca-malate complexes at / = 0.1 M

and 25 °C.

[Ca2^], [H2A]t pH -E [Na+] [Ca2+]^ [CaA]^ [A2-]^ K

X 103 M x103M mV X 102 aj X 103 X 103 ,\i X 103 M xlO-2

2.010 1.010 6.04 47.3 9.3 1.688 0.322 0.659 2.89

3.140 4.040 6.46 45.7 8.7 1.949 L191 2.801 2.18

4,019 3.030 6.33 42.0 8.5 2.644 1.375 1.618 3o22

5.024 6.010 6.51 41.4 7.9 2.789 2.235 3.72 2.16

6.029 5.050 6.49 39.4 7.7 3.297 2.732 2.28 3.64

7.002 7:979 6.64 39.8 7.1 3.197 3.805 4.13 2.88

8.007 6.969 6.60 37.3 6.9 3.908 4.009 2.84 3.70

9.043 9.999 6.73 36.9 6.3 4.060 4.983 4.97 2.47

Mean = 2.89

logK = 2.46

Literature values: log K = 2.06 at / - 0.16

= 2.66, 2.24 at / = 0

Table 9. Formation constants of Ca—citrate complexes at / = 0.1 M

and 25 °C.

[Ca2+]^ [Us Ah pH -E [Na^ [CaA-]e K

xlO% xlO% mV X lO^M xlO% xlO% xlO"

6.000 5.000 6.62 47.5 6.7 1.721 4.279 0.616 4.04

6.000 7.000 6.88 56.5 6.1 0.825 5.175 1.665 3.77

8.000 7.000 6.67 46.8 5.5 1.843 6.157 0.730 4.58

8.000 10.000 6.98 58.9 4.6 0.699 7.302 2.511 4.17

10.000 8.000 6.61 42.7 4.6 2.576 7.424 0.489 5.89

10.000 9.000 6.71 46.6 4.3 1.895 8.105 0.785 5.45

10.000 10.000 6.78 50.2 4.0 1.420 8.580 1.270 4.76

Mean = 4.66

logK = 3.67

Literature values: log K = 4.68, 4.90 at / = 0

= 3.17 at / = 0.15
ANALYTICAL STUDIES 333

Table 10. Formation constants of Ca-DCTA complexes at / = O.IM

and 25 °C.

[Ca2'], [H4A]/ pH -E [Na'l [Ca2+]^ [CaA^"V K

X lO^M mV X 10 X lO^M X lO^Al xl0l3 X 10-^

o.UUo 7 noR Af< Q 7 n 1 ftO^ U. ZiU 1 D. 0 1 o.UUd ft f\r\(^ Q no/i y .UU4 A 97 /1ft 7 I.OOD a AA9 ft Qlft A ft7 4.01 7.003 5.996 4.38 44.6 7.3 2.159 4.844 6.274 3.58

7.003 7.994 4.36 53.1 7.1 1.073 5.930 10.030 5.51

5.997 5.007 4.38 46.4 7.7 1.857 4.140 4.973 4.65

5.997 7.006 4.40 52.4 7.5 1.134 4.863 1.321 3.25

4.994 3.997 4.34 45.5 8.1 1.988 3.006 4.357 3.47

4.994 5.996 4.39 56.4 7.9 0.795 4.119 10. 132 5.22

Mean ~ 4.48

logK' = 12.65

Literature values: log K = 12.3, 12.5 13.15 at / = 0.1

thus, its response time is not critical within reasonable limits. This same

approach is now being successfully applied to kinetic investigations using

the more sluggish liquid membrane electrodes.

The first really comprehensive investigation undertaken was the kinetic

study [11] of the exchange reaction between Ag(I)-EDTA and Ni(II).

This study, which yielded the mechanisms (where Y denotes EDTA)

Ni-^+ + AgY^- -!^ NiY^- + Ag+ (5) Ni^+ + AgHY-- NiY^- + Ag+ + H+ (6) Ni-^-hHY-^- NiY'-^- -h (7) Ni-^+ + Y4- NiY^- (8) for the 9.2-10.2 pH region and

NiOH + H- AgY-^- NiY-- + Ag^ + OH" (9) NP^ + AgY-^- NiY-^- + Ag+ (10)

for the pH 10.8 to 1 1.4 range, was conducted by continuously measuring

the activity of silver(I) with a cation sensitive glass electrode and demonstrates the use of such electrodes in homogeneous kinetic systems.
334 ION-SELECTIVE ELECTRODES

Figure 9. Response of Orion liquid membrane ClOj selective electrode to CIO4 activity

at various temperatures.
ANALYTICAL STUDIES 335

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336 ION-SELECTIVE ELECTRODES

These two studies stimulated our interest in using the newer liquid

membrane and solid crystal electrodes for quantitative rate measurements. Because of the importance of Ca-+-EDTA reactions to analytical

chemistry we [8] undertook an investigation of the reaction

Ca^^ + Mg-EDTA ^ Ca-EDTA + Mg^+ (11)

in conjunction with the study of Ca-EDTA complexes already discussed

above.

For this purpose, we used the Orion liquid type Ca-+-selective elec- trode with careful attention to possible interferences and control of

kinetic conditions so as not to exceed the effective response time limits of

the overall measuring system. By carrying out the kinetic study with Ca-+

in excess, useful data could be obtained from the early portion of the reaction course. Figure 10 shows some of the rate data as a function of the

5.0 — 4.0

•o

X

o

3.0

2.0

1.0' ' ' ' '—

0 1.0 ^0 3.0 4.0

[h"^]x 10*^ (M)

Figure 10. Ca^+-Mg-^ + EDTA exchange reaction. pH dependence of rate constant. Conditions as in Reference [8].
ANALYTICAL STUDIES 337

solution pH and gives an indication of the precision and accuracy of the

method. From these and similar measurements it was possible to arrive at the overall mechanism

Ca2+ + Mg(II)Y CaY + Mg^+ (12)

Ca2+ + Hy-

^

CaY + H- (13)

Ca2+ + Mg(II)HY+ CaY + Mg-^+ + (14)

Ca2+ + Y2- CaY (15)

where A;/, /://, /:///, and have the values of 2.7 X 10^ M-^ sec-^2.3x 10^ M-^ sec-i, 1.3 X lO'i M-- sec-', and 2 x lO^M"' sec"', respectively. This

mechanism may be compared with the paths for the Ag(I)-EDTA +

Ni(II) reaction, above, and shows that liquid membrane electrodes can

also be used for the study of moderately rapid reactions.

Because of their rapid response and minimal interferences, solid crystal

membrane electrodes can be easily used for kinetic studies. The

fluoride-selective electrode is particularly useful in this connection

because the continuous measurement of fluoride activity in solution is a

difficult analytical problem. We, therefore, used [5] this electrode to measure the rates of formation of the monofluoro complexes of iron(III) and

aluminum(III). The first system was chosen because some kinetic measurements had already been done using optical techniques and could,

thus, give a good indication of the reliability of the new method; the

second system had never been studied from the kinetic viewpoint,

because of measurement difficulties associated with conventional

techniques, and thus provides a challenging test of the electrode method.

Figure 1 1 is typical of the emf vs. time curves recorded during the reaction between ferric and fluoride ions. The potential of the fluoride-ion

selective electrode becomes progressively more positive with respect to the calomel electrode indicating a decrease in the free fluoride ion concentration resulting from the formation of FeF-+. From a series of experiments carried out at different initial H^, Fe-^+, and F" concentrations, the

rate constants shown in Table 12 could be obtained and the general

results yielded the mechanism

Fe"^+ + F- ^ FeF-^+ (16)

Fe^++HF ^FeF-+ + H+ (17)

under the conditions used, any contribution from HF.j could be neglected.
338 ION-SELECTIVE ELECTRODES

= 0.06887.V/. (3) [H-]=0.03722.V/

The formation of AlF-~ is very much more complicated than that of

FeF-~ and. as Figure 12 shows, the rate of formation is quite slow. For

this reason, the kinetic data were analyzed using the initial rate method

(results in Table 1 3 ) and led to the overall rate law

Ai[H-] [AF^] [F-] ^A„[AF-] [F-] + Ani[AP-] [F"]^ (18)

where ki, kn, and km are 346 M~- sqq-K 5 M"^ sqc-\ and 1.03 x 10-^--

sec"'. respectively. This rate law corresponds to the proposed mechanism

A13- + HF ^ AlF^- + H- (19)

'A1(H20)=^- + F- ^ AlOH- -fHF (20)

AlOH^' + HF ^AlF'+HoO (21)

which is confirmed also bv independent chemical evidence.
ANALYTICAL STUDIES 339

Table 12. Values of rate constant K' for the formation of FeF^+ at 25 °C and at an ionic strength of 1.0 M.

[H+1 M [Fe^+ltxlO^M [F"]; x 10^ M K' x IQ-^ (M-^ sec"!)

0.1316 1.584 0.9259 10.80, 10.90

0.1316 0.8223 0.7692 11.21, 12.59

0.1316 1.584 0.7407 10.73, 10.40

0.1316 0.8223 0.3846 11.19, 11.43

0.1316 1.584 0.3704 10.24, 10.05

0.1316 0.8223 0.1923 11.07, 10.46

0.1316 1.584 0.1852 9.92, 9.52

0.06887 1.584 0.9259 7.24, 7.20

0.06646 0.8223 0.7692 8.28, 8.84

0.06887 1.584 0.7407 7.62, 7.98

0.06646 0.8223 0.3846 7.75, 8.30

0.06887 1.584 0.3704 6.71, 6.69

0.06646 0.8223 0.1923 7.44, 8.48

0.06887 1.584 0.1852 6.63, 6.64

1 O. 1 U 0.03359 0.8223 0.7692 6.47, 6.79

0.03722 1.584 ' 0.7407 6.04, 5.22

0.03e359 0.8223 0.3846 5.98, 6.27

0.03722 1.584 0.3704 4.70, 4.81

0.03359 0.8223 0.1923 5.24, 5.40

0.03722 1.584 0.1852 4.71, 4.60

While the use of ion-selective electrodes for such rate studies holds

considerable promise in itself, one should not conclude that the range of

application in kinetics is restricted to straightforward rate measurements.

Recently for example, we [12] used the fluoride ion electrode, less directly, in a kinetic study of the iron(I I l)-iodide reaction in fluoride

media where fluoride is not involved as one of the reactants.
340 ION-SELECTIVE ELECTRODES

Figure 12. A1F-+ formation as function of time. LaFa type F" electrode vs. saturated calomel reference. Runs 1-3, show increasing F'/Al^+ratio.

It had been known that fluoride ions inhibit the reaction between

iron(lll) and iodide, but there was no way to distinguish between the main

alternative mechanisms, e.g., one in which the inhibition results because

FeF"+ reacts more slowly with I" than Fe^+ or one in which the inhibition occurs because FeF-+ is unreactive toward and the presence of F"

lowers the equilibrium concentration of Fe'^+ available. Work on the

analogous reactions involving FeCl-+ or FeBr-+ had favored the first al- ternative. By monitoring the concentration of free fluoride ion during the

reaction and using our knowledge of FeF-+ formation constants, we were

able to demonstrate, however, that the second mechanism is operative,

i.e., that FeF-+ does not oxidize iodide ion. This, then, is an example of

the use of ion-selective electrodes as a diagnostic tool in the characterization of reaction mechanisms — a use which should become more popular as kineticists learn about the capabilities of these electrodes. V. Analysis

While this review is primarily devoted to physico-chemical studies, it would be a disservice to the potentialities of ion-selective electrodes not

to include some comment on their usefulness in chemical analysis. Obviously, that usefulness is very great indeed and surely accounts for the

bulk of the electrodes in use today.
ANALYTICAL STUDIES 341

Table 13. Initial rates of formation of A1F^+ at 25 °C and at an ionic

strength of 1.0 M.

Acid LAi J X iU IVl Lr J X iU Ivi It ate X lU Corrected ra cone. (M sec~^) (M sec"^)

0.1316 M 1.357 0.3211 2.277 1.913

!f 0.7245 0.3445 1.343 1.129

If 1.358 0.1587 1.025 0.882

fT 0.3790 0.3640 0.682 0.561

Tf 0.7298 0.1738 0.604 0.517

!f 1.360 0.07917 0.426 0,363

ff 0.3783 0.1809 0.340 0.293

!T 0.7308 0.08687 0.253 0.215

f! 0.3794 0.09068 0.144 0.124

0.06353 1.359 0.6627 2.913 1.847

ff 1.362 0.3340 1.491 1.106

ff 1.360 0.1624 0.623 0.476

0.05849 0.7214 0.7591 1.793 1.090

ff 0.7275 0.3815 0.833 0.584

ff 0.7301 0.1917 0.400 0.302

0.05568 0.3736 0.8371 1.009 0.582

ff 0.3768 0.4186 0.467 0.319

ff 0.3791 0.2109 0.219 0.161

0.0408 1.332 0.9414 3.702 1.855

ff 1.360 0.5063 1.628 0.923

ff 1.357 0.2414 0.611 0.365

0.03412 0.7222 1.285 2.868 1.172

ff 0.7266 0.6411 1.028 0.487

ff 0.7206 0.2900 0.393 0.226

0.0304 0.3615 1.457 1.586 0.529

ff 0.3636 0.7001 0.574 0.263

ff 0.3731 0.3554 0.259 0.144
342 ION-SELECTIVE ELECTRODES

The accompanying Tables (14 and 15) indicate something of the

present range of application of ion-selective electrodes. That range ex- tends from measurements of industrial and geological samples to deter- minations carried out in actual living beings. The promise of ion-electrodes in clinical and chemical laboratories, perhaps in conjunction with

automated equipment and computer processing, seems especially great.

It is my personal opinion that ion-electrodes represent an exciting new

tool for chemical measurement and that their use will significantly extend

the frontiers of scientific investigation.

Table 14. Analysis by direct potentiometry using ion— selective

electrodes.

A. Inorganic systems

Synthetic samples

Synthetic samples

Synthetic samples

Synthetic samples

Bone

Minerals

Water

Tungsten

Ion determined

( boron)

Na

Conditions and remarks

Orion 92-07 electrode, direct

potentiometry after conversion

and ion exchange; NO^ and

I" interfere Modified Orion F~ electrode; microanalysis by linear nullQ point technique; 10 to 2 X 10"^ M F~ in 10 ^il samples

Orion electrode; 10""^ to 10"^

M F~ using standard addition

technique; interferences masked

with phosphoric acid

-6.7

Ref

[13]

[14]

[15]

Orion electrode; F to 10 M [16]

using 60% ethanol medium

Orion 94—09 electrode; deter- [17]

mination after ashing of bone

Orion electrode; determination [18]

in fluorite, cryolite, topaz, etc. GEA 28 Na+ glass electrode; [19]

direct Na^ determination in 0.004-25 ppm range; pH control with ammonia vapor

Orion electrode; dissolution of [20]

sample by fusion; determination

in 2—100 ppm range
ANALYTICAL STUDIES 343

Table 14. Analysis by direct potentiometry using ion-selective

electrodes, (continued)

A. Inorganic systems

Chromium plating

solutions

Synthetic samples

Synthetic samples

Synthetic samples

Synthetic samples

Synthetic samples

Synthetic samples

Synthetic samples

Synthetic samples

Soils

Ion determined Conditions and remarks Ref

F~ Orion F~ electrode; direct [21]

determination of plating bath

samples

NOJ Evaluation of Orion NO3 [22]

electrode; pH range 4—7

Ca^^ Evaluation of Orion Ca^+ [ 23]

electrode; gives cation selectivity

ratios, other interferences

Macrotetrolide impregnated [24]

membrane electrode; response

not Nernstian but good to Na^ selectivity

ClOJ" Evaluation of Orion CIO7 [9] electrodes; pH range selectivities, dynamic response

S" Evaluation of Orion S" [6] electrode; direct potentiometry

and titrations F~ Orion F~ electrode in acidic [4] media; effect of HE and HF^

formation

Ca^^ Evaluation of Corning and [8] Orion liquid membrane Ca

electrodes; analytical, equilibrium

and kinetic studies

Cu^+ Evaluation of Orion Cu^+ [7] electrode; pH effect, study of

complexes

K+ Beckman 78137 V electrode; [25] cone > 10"^ M, troubled by

interferences (Na^, NH4 )
344 ION-SELECTIVE ELECTRODES

Table 14. Analysis by direct potentiometry using ion— selective

electrodes, (continued)

Ion

A. Inorganic systems determined Conditions and remarks Ref

Soils and slurries Na^

Clay suspensions and Na^

marine muds

Boiler water Na"*"

Acidic sol systems Na^

Basin waters Na^

Sea water Ca^^

Sea water Mg^^

Synthetic samples F"~

Synthetic samples NH^

(urea,

urease)

Synthetic samples Rj^NH4,j^

Synthetic samples I~

Synthetic samples Cl~, Br~

Synthetic samples Ag"*"

Beckman 78137 V electrode, 1.6 [26] to 500 meq/1; 0.2% relative

agreement with flame photometry

[27]

Beckman 78178 V electrode; [28,

ppb level , continuous 29]

monitoring

Beckman 78137 V electrode; [30]

12-300 ppm Na+ 5.7% relative

deviation compared to flame

photometry

Beckman 78178 electrode; 10 [31] to 1.3 X 10^ ppm Na+

Orion Ca^^ electrode; Mg2+ [32] interferes; 0.3 mV reproducibility

Orion Mg2+ electrode [33]

Orion 94-90 F" electrode, only [34]

0H~ interferes seriously

Beckman 39137 electrode; 3% [35]

relative accuracy in millimolar range Beckman 39137 electrode; [36]

response is size dependent

Agl membrane electrode, [37]

Nernstian response to 10" M l~

AgCl and AgBr membrane [38]

electrodes

Beckman 39278 electrode; little [39]

interference from alkali metal ions
ANALYTICAL STUDIES 345

Table 14. Analysis by direct potentiometry using ion— selective

electrodes, (continued) Ion

A. Inorganic systems determined Conditions and remarks Ref

Synthetic samples Ag^

B. Biological and

living systems

Blood

Electronic Instruments, Ltd. [40]

GNA 23 electrode; good response

to 10~^ M Ag+, puzzling

interference by iron (II). Ion determined

Na\ K+

H+, cr

Conditions and remarks Ref

Urine Na^

Serum, plasma, urine, Na^

cerebrospinal fluid Bile Na+ , K+

Tissue extract Na^,

Nerve and muscle Na^,

tissue

Kidneys Na+,

Cerebral cortex Na^,

BodyHuids Na+, K+

Automated determination using [41]

glass and silver electrodes in flow system; automatic computation

Beckman 39278 electrode; good [42]

agreement with flame photometry

No interference from proteins [43] or uric acid

Flind Na^ association

Study of Na^, binding in brain extract Uses microelectrodes to follow

ion flux across cell membranes

[44]

[45,

46]

[47]

Measurement of ion activities [48]

in single kidney tubules

Analysis of cerebrospinal fluid [49] as function of physiological variables

variables

Determination of Na^ and [50]

using differential measurement with

with analog computer
346 ION-SELECTIVE ELECTRODES

Table 15. Potentiometric titrations using ion—selective indicator

electrodes.

Ion determined Titrant

clo:

Ag+

Ag+

K+, Cs+,

Rb+,NH4+^

Ag^

ICa2+

tetraphenylarsonium

chloride

tetraphenylantimony

sulfate

2+ Ca

MgCL

CNCa( 30)4)2

Ca(B0 4)2

Zn{SiF6)

AgC104

EDTA

Conditions and remarks

Orion 92-81 electrode; pH 4-7

range

Orion F~ electrode; involves

extraction with chloroform

Orion F~ electrode; tests usefulness of various titrants and conditions

Uses NAS27_8 electrode; good

accuracy but smaller A E at end

point than same titration with Ag

metal electrode

Only AgCN end point (not Ag(CN)2

end point) is seen owing to moderate

Ag^ sensitivity of NAS27_8 electrode

Uses NAS33_5 electrode; 0.25%

relative accuracy at 30 mg level Beckman 39137 electrode; 10-110 mg

range, accuracy limited by volumetric

technique; sharp "S"— shaped

titration curves Uses NAS27_8 electrode; determination of 2—160 mg in water-methanol

solvent with 0.1% relative accuracy;

Ref

[51]

[52]

[53]

[39,

54]

[54]

[55]

[56]

[57]

Ca^+, Mg'^^, Al'^^ interfere owing to reaction with F~

Agl membrane electrode; 0.2% relative [37]

accuracy at 10~^ M I~ level with

~400 mV break at end point

Orion 92-20 Ca^^ electrode; pH [58]

adjusted to 11 with NH4OH, rather poor end-point break

i3+
ANALYTICAL STUDIES 347

Table 15. Potentiometric titrations using ion-selective indicator

electrode, (continued)

Ion determined Titrant Conditions and remarks Ref

F- La(N03)3 Orion 94-09 F" electrode; about [34]

120 mV end-point break for 0. 1 M

solutions, good agreement with

calculated end point

VI. References

Rechnitz,G. A. Chem. Eng. News 43 (25). 146(1967).

Eisenman, G., Anal. Chem. 40, 3 1 0 ( 1 968). Rechnitz, G. A., and Kugler, G. C, Anal. Chem. 39, 1682 (1967). Srinivasan, K., and Rechnitz, G. A., Anal. Chem. 40, 509 (1968). Srinivasan, K., and Rechnitz, G. A., Anal. Chem. 40, 1818 (1968). Hseu, T. M., and Rechnitz, G. A., Anal. Chem. 40, 1054 (1968). Rechnitz, G. A., and Lin, Z. P., Anal. Let. 1, 23 (1967). Rechnitz, G. A., and Lin, Z. P., Anal. Chem. 40, 696 (1968). Hseu, T. M., and Rechnitz, G. A., Anal. Let. 1, 629 (1968). McClure, J. E., and Rechnitz, G. A., Anal. Chem. 38, 136 (1966). Rechnitz, G. A., and Lin, Z. P., Anal. Chem. 39, 1406 (1967). Srinivasan, K., and Rechnitz, G. A., Anal. Chem. 40, 1955 (1968). Carlson, R. M., and Paul, J. L., Anal. Chem. 40, 1292 (1968). Durst, R.A., Anal. Chem. 40, 93 I (1968). Baumann. E. W., Anal. Chim. Acta 42, 1 27 (1968). Lingane, J. J., Anal. Chem. 40, 935 (1968).

Singer, L., and Armstrong, W. D., Anal. Chem. 40, 613 (1968). VanLoon, J. C, Anal Lett. 1, 393 (1968). Hawthorn, D., and Ray, N. J., Analyst 93, 158 (1968). Raby, B. A., and Sunderland, W. E., Anal. Chem. 39, 1304 (1967).

Prant. M. S.. Plating, June 1967. Potterton, S. S., and Shults, W. D., Anal. Lett. 1, 1 1 (1967). Ross, J. W.. Science 156. 1378 (1967). Stefanac, Z., and Simon, W., Microchem. J. 12, 125 (1967). Mortland, M. M., Quart. Bull. Mich. Agric. Exp. Station 43, 49 1 (1 96 1). Bower, C. A., Soil Sci. Am. Proc. 23, 19 (1959): 25, 18 (1961).

Siever, R., and Garrels, R. M., Kanwisher, J., Berner, R. A., Science 134, 1071 (1961). Jones. R. H., Ind. Water Eng. 1 . March-April 1964. Mattock. G., Anal. Chem. Proc. Intern. Symp. 59, 247 ( 1963).

Taulli, T. A., Anal. Chem. 32, 186 (1960). Truesdell, A. H., Jones, B. F., and VanDenburgh, A. S., Geochim. Cosmochim. Acta

29, 725 (1965). Thompson, M. E., and Ross, J. W., Science 154, 1643 (1966). Thompson, M. E., Science 153, 866 ( 1 966). Prant, M. S., and Ross, J. W., Science 154, 1553 (1966). Katz, S. A., and Rechnitz, G. A., Z. anal. Chem. 196, 248 (1963).
348 ION-SELECTIVE ELECTRODES

[36] Rechnitz, G. A., and Kugler, G., Z. anal. Chem. 210, 174 (1965).

[37] Rechnitz, G. A., Kresz, M. R., and Zamochnick, S. B., Anal. Chem. 38, 973 (1966).

[38] Rechnitz, G. A., and Kresz, M. R., Anal. Chem. 38, 1786 (1966).

[39] Budd, A. L.J. Electroanal. Chem. 5. 35 ( 1 963).

[40] Bishop, E., and Dhaneshwar, R. G., Analyst 88, 424, 442 (1963).

[41] Dahms, H.,Clin. Chem. 13,437 (1967).

[42] AnnincJ. S.,Clin. Chem. 13. 227 (1967).

[43] Moore, E. W., and Wilson, D. W., J. Clin. Invest. 42, 293 (1963).

[44] Diamond. J., J. Physiol. (London) 161. 442 ( 1 962).

[45] Ungar.G..Cytologia 1.622 (1959).

[46] Ungar, G., and Romano, D. V., Fed. Proc. 18, 162 (1959).

[47] Hinke..L A.. Nature 184, 1 257 ( 1 959): J. Physiol. 156.314(1961).

[48] Khuri, R. N., et ai, Amer. J. Physiol. 204, 743 (1963).

[49] Portnoy, H. D., Thomas, L. M., and Gurdjian, E. S., Arch. Neurol. 8, 597 (1963).

[50] Friedman, S. M., and Bowers, F. K., Anal. Biochem. 5, 471 (1963).

[51] Baczuk, R. J., and DuBois, R. J., Anal. Chem. 40, 685 (1968).

[52] Orenberg, J. B., and Morris, M. D., Anal. Chem. 39, 1776 (1967).

[53] Lingane..!. J.. Anal. Chem. 39.881 (1967).

[54] Geyer, R., Chojnacki, K., and Stief, C, Z. anal. Chem. 200, 326 (1964).

[55] Geyer, R., and Grank, H., Z. anal. Chem. 179, 99 (1961).

[56] Rechnitz, G. A., Zamochnick, S. B., and Katz, S. A., Anal. Chem. 35, 1322 (1963).

[57] Geyer, R., Chojnacki, K., Erxleben, W., and Syring, W., Z. anal. Chem. 204, 325

(1964).

[58] Instruction Manual. Model 92-20 Electrode. Orion Research. Inc., Cambridge.

Mass.. 1966.
CHAPTER 10

INDUSTRIAL ANALYSIS AND CONTROL

WITH ION-SELECTIVE ELECTRODES

Truman S. Light

The Foxboro Company

Foxboro, Massachusetts

I. Introduction

Industrial analysis is a term applied to analytical composition information derived from a continuous signal which may be used for monitoring

or control purposes. Industrial analysis ("continuous analysis," "on-line

analysis" or "process analysis") for the most part derives its principles

from laboratory analytical practices and procedures. However, laboratory analytical instrumentation is seldom suitable for direct use in the

plant. The industrial analysis instrument continuously receives samples

from the process or environment and continuously sends out a signal with

information about the composition of the sample. A person must bring a sample to the "automatic" laboratory instrument, read the answer, in- terpret the results and take appropriate action. The process analytical in- strument is not privileged to sit with the chemist in an air-conditioned

laboratory, but must receive its sample "as is" from a process which often runs at extreme temperatures and pressures.

It is not surprising that ion-selective electrode applications should ap- pear promising to the industrial analytical field. Ion-selective electrodes

may be placed into a process solution and will transmit an electrical signal that characterizes the composition of the solution. This information is obtained rapidly and may be utilized to operate a controller, or as a process

computer input. Large-scale industrial production has created waste

problems. The composition of plant effluents, both liquid and gaseous,

have become of considerable concern. In many cases, ion-selective elec- trodes could permit continuous analysis of these effluent streams. The present paper discusses the principles and operation of ion-selective electrodes related to their use in industrial analytical instrumentation.

Many applications for ion-selective electrodes have been recognized and

developed since the first industrial uses were discussed two years

ago [1].

II. Ion-Selective Electrodes

An ion-selective electrode is defined simply as an indicator or measuring electrode with a relatively high degree of specificity for a single ion or 349
350 ION-SELECTIVE ELECTRODES

a class of ions. The glass electrode for pH measurement (hydrogen ion activity) was the earliest ion-selective electrode to attain widespread use. It became commercially available with accompanying instrumentation in the 1930's. The theory and application of the glass pH electrode for both

laboratory and industrial use have been well documented [2,3]. Around

1959, two more ion-selective electrodes of the glass electrode family

became commercially available. One of these was for sodium, the other

for potassium, silver and other univalent cations. The glass electrode

family has also been thoroughly treated in the literature [4,5]. Beginning

in 1966, two new classes of ion-selective electrodes, solid-state and liquid

ion exchange, were introduced. New electrodes are still being introduced

and, consequently, the literature is in a state of growth. Detailed discussion of the construction, characteristics, limitations, and applications of

these electrodes are presented elsewhere in this publication, e.g., Chapters 2 and 3. In Table 1, a current list of the commercially available

laboratory model ion-selective electrodes is given with some of their chemical limitations. This list, which can be divided into three classifica- tions—glass, solid-state and liquid ion exchange — now numbers over 20 electrodes.

Table 1. Commercially available ion—selective electrodes, 1969.

Electrode

designated for Class^ pH range Principal interferences

Bromide S 0-14 CN", I", S=

Cadmium S 1-14 Ag+, Hg++, Cu++, Fe++. Pb++

Calcium L 5.5 - 11 Zn++, Fe++, Pb++,

Cu+-^, Ni++

Chloride S 0-14 Br~, I~, S=, CN",

SCN",NH3

Chloride L 2-10 ClOj, I~ NO^, Br",

0H~, OAc~, HCO^,

S0|, F~

Cyanide S 0-14 S=, I~

Cupric S 0-14 Ag+, Hg++, Fe^+
INDUSTRIAL ANALYSIS AND CONTROL 35]

Table 1. Commercially available ion—selective electrodes, 1969

(continued).

Electrode

designated for Class^ pH range Principal interferences

Fluoride S 0 -8.5 OH"

Fluoroborate L 2 - 12 I~, N05", Br~, OAc~,

HCO5-

Iodide S 0 - 14 S=,CNLead S 2 - 14 Ag+,Hg++,Cu^,Cd^+,

Fe++

Lead L 3.5 - 7.5 Cu++, Fe++, Zn++,

Ca++,Ni++,Mg++,

Nitrate L 2 - 12 C10r,I~, C10§", Br",

S=,N02",CN-, HCO3",

CI , OAc , CO3,

S20^, SOi

Perchlorate L 4 - 10 0H~, r,N05"

Hydrogen (pH) G 0 - 14

ORP (OX-RED POT.) S 0 - 14 All redox systems

Potassium G 7 - 13 H+, Ag^ NHJ, Na+, Li+

Silver S 0 - 14 Hg^^

Silver G 4 -8 H^

Sodium G 6

1 o Ag+, H+, Li+,

Sulfide S 0 - 14 Thiocyanate s 0 - 14 r, Br- cr, S2O5,

NH3

Water Hardness L 5.5 - 11 Zn+-^, Fe++, Cu-^+,Ni++

Ba++, Sr++ = Glass; L = Liquid Ion Exchange; S = Solid State.
352 ION-SELECTIVE ELECTRODES

Application of any of these electrodes to a given problem should be

made only after consideration of the manufacturer's and other literature,

and the physical and chemical limitations of the electrodes. The principles

of construction of these three classes of electrodes may be seen in Figures

1 and 2. In Figure 1, the construction of the glass electrode with its glass

INTERNAL

FILLING SOLUTIONINTERNAL—^

REFERENCE ELECTRODE GLASS MEMBRANE ZSILVER SULFIDE MEMBRANE

SOLID INTERNAL

SILVER WIRE OR BILLET

CONVENTIONAL

GLASS

pH ELECTRODE

SILVER SULFIDE

MEMBRANE

ELECTRODES

-SILVER SULFIDE CONVENTIONAL

SILVER , SILVER

SULFIDE ELECTRODE

Figure 1 . Construction of glass electrode and silver sulfide membrane electrode.

Internal

Aqueous

Filling

Solution

Ag-AgCI

Reference

Electrode

Porous

Membrane

Liquid Membrane

Ca+ + Electrode

Ion

Exchanger

Reservoir

Liquid Ion

Exchange

Layer

Figure 2. Construction of liquid ion exchange electrode (Orion Research Inc.).
INDUSTRIAL ANALYSIS AND CONTROL 353

ion-selective membrane, internal filling solution and internal reference

electrode is compared with the solid-state sulfide ion electrode. Also

shown in Figure 1 is a slightly different form of the sulfide ion electrode

with a solid internal contact to the membrane [6]. This form is of special

interest to industrial process monitoring because it minimizes the pres- sure and temperature limitations imposed upon electrodes with aqueous

internal solutions. The electrode is also more stable due to the elimination

of the internal solution/solid interface. Finally, Figure 1 shows a conventional silver-silver sulfide wire electrode which is susceptible to oxidation-reduction potential errors [7]. Figure 2 shows a cross-section

view of the liquid ion exchange electrode. These electrodes have more

severe chemical and physical limitations than the glass or solid-state elec- trodes; yet these limitations are more than offset by the fact that the liquid

ion exchange electrodes are able to measure certain cadons and anions

that have not previously been accessible by direct potentiometry [8].

III. Nernst Equation and Modifications

The Nernst equation provides the basic means of interpreting the

potentiometric output of an ion-selective electrode in terms of the ion activity in the solution^:

E=E° + {0A9S4\Tln) log ai (1)

A. Selectivity Coefficient

The simple form of the Nernst equation, Equation (1), explains most of

the performance of the pH sensitive glass electrode. With the introduction

of additional ion-selective glass electrodes, solid-state and liquid ion

exchange electrodes, it was found that many electrodes responded to ions

other than those for which they were designated. A modified form of the

Nernst equation is now commonly used to describe the performance of

ion-selective electrodes [4,5].

E = E° +{0.19S4^1TIn) log {ai + Kija^"^. . .) (2)

where Kij is the selectivity coefficient of the interfering ion "j'' with

respect to the designated ion and "m" may be an integer or fraction. The selectivity coefficient "A^,/' becomes a useful quantitative tool to predict whether a given ion-selective electrode may be used in the

presence of known impurities. Table 1 indicates the principal inter- ferences for most of the presently available ion-selective electrodes. For

'Nomenclature is appended to this chapter.
354 ION-SELECTIVE ELECTRODES

quantitative evaluation of the selectivity coefficient, it is usually necessary to consult the manufacturer's literature. For example, a common form

of the sodium sensitive glass electrode is made from a glass designated as NASii-18. For this glass, A^nhh is approximately 30 [9]. The electrode is then understood to be 30 times more sensitive to the hydrogen ion than to the sodium ion, even though it is designated as sodium sensitive. If the

sodium electrode of this example is to be used to measure a one millimolar

solution of sodium ion with an accuracy of 3%, then the hydrogen ion concentration must be less than 10~W (pH greater than 6). For direct measurement of sodium ion activity, it follows that the sodium ion electrode

is more useful in alkaline solutions than in acid solutions. However, Equation (2) also indicates the possibility of using multiple ion-selective elec- trodes. For example, if sodium ion must be measured in acid solutions, an

additional glass electrode may be introduced to measure the pH of the

solution and from Equation (2) and the known selectivity coefficient,

^NaH' the corrected activity of the sodium ion in the acid solution may be

calculated.

B. Temperature Coefficients

The fundamental form of the Nernst equation given in Equation (1) is valid only at constant temperature.

The temperature variation of ion-selective electrodes may be described

by differentiating Equation (1) with respect to temperature [ 10]

:

idE/dT),n={dE°ldT)th + (0.1984lMj log ai +

(0. 1 984 IJ/nj (d log aJdT) (3) The overall effect of changing the temperature of an ion-selective elec- trode immersed in a solution, {dEldT)th. may be better understood if it is divided into three separate contributions:

1. {dE°/dT)th is the standard temperature coefficient of the ion-selective electrode. This is a quantity that is characteristic of the particular

ion-selective electrode, or of the ion-selective electrode and its reference

electrode in a cell. Very little has been reported to date on temperature

coefficients for lon-selective electrodes. In such cases as the sulfide ion

electrode, the temperature coefficients of ion-selective electrodes and

classical electrode systems coincide [7]. In other cases, such as the

glass pH sensitive electrode, the standard temperature coefficient is a function not only of the electrode's membrane material but also of

the internal electrode and the internal filling solution. Here the standard

temperature coefficient may depend upon the manufacturer's design

and individual batch variations. The temperature coefficients may be
INDUSTRIAL ANALYSIS AND CONTROL 355

minimized by adjustment of internal electrode composition and matching

to the reference electrode.

2. (0.19841/Azj log di is the temperature coefficient slope term of the

Nernst equation. This is the temperature correction usually performed by

the manual or automatic temperature compensator of the modern pH or

ion-selective meter. This temperature coefficient term corrects for the

temperature slope change of the log ai vs. E relationship of the Nernst

equation. A frequently occurring error in using pH or ion-selective meters

is caused when it is assumed that this is the only cause for variation of observed emfs with temperature.

3. (0.1984ir/«j(d log dildT) is the solution temperature coefficient term. The activity of an ion may be affected by its activity coefficient and

for weak or complex forming electrolytes by its equilibrium relationships.

Since activity coefficients and equilibrium constants may each have temperature coefficients of their own, the "solution temperature coefficient"

term may become quite complex. For the pH standard solutions used in the calibration of pH meters, Bates and coworkers of the National Bureau

of Standards have painstakingly prepared temperature coefficient tables

[11]. The establishment of reference materials, solutions, and the temperature coefficients for ion-selective electrodes largely remains to be

done.

Another small, but measurable temperature coefficient effect is contributed by the third term for the "solution temperature coefficient." The

Nernst equation is valid for the use of any suitable units for the activity

term Concentration or activity expressed in "molal" units are dependent on mass and are, therefore, temperature independent. However, it is more common to express concentration in molar units which are volume

(and, therefore, temperature) dependent. Thus, the latter temperature

coefficient term also includes the dilution correction caused by the expansion of most solutions upon heating. Quantitatively, this would be measured by the temperature dependence of the solution density.

C. Accuracy

The accuracy of measurements derived from any analytical system is a composite of all contributing variables. There are several possible sources of error in ion-selective electrode measurement. These include:

the measuring electrode, the reference electrode, including the liquid

junction potential, the measuring system (converter and recorder), temperature, solution errors, and the Nernst equation relationship.

The relationship between overall emf errors, AE, and concentration, C,

may be derived from the Nernst equation. Equation (1), by taking the
356 ION-SELECTIVE ELECTRODES

derivative with respect to concentration:

^E = (0.2568/A2j (100 AC/Cj (mV at 25 °C) (4a)

AE = {0.256Sln) (RE) (4b)

A plot of Equation (4b) is given in Figure 3. The relative error in concentration, RE, is dependent only on the error in the emf and is independent of the concentration range, and of the size of the sample being measured. For an electrode responding to univalent ions, an overall error of

FOR ELECTRODES OBEYING NERNST

EQUy\TION AT 25° C E=E- + {59.l6/n) logC

y

AE, (mv)=(0.2568/n (RE) 4

UJ 2 <

^ 10 20 30 40 50 60 70 80 90 100 110 120 00 RE, PERCENT RELATIVE ERROR IN CONCENTRATION

Figure 3. Theoretical error in potential as a function of relative error in concentration.

1 mV corresponds to a 3.9 percent relative error in concentration: for an

electrode responding to divalent ions, the relative error is 7.8 percent per

mV.

Measuring instruments using ion-selective electrodes have become

commercially available with an accuracy of ±0.1 mV. They are capable

of measuring through the high impedance characteristic of the electrodes.

Glass electrodes for pH have almost perfect response, following the

Nernst equation over a wide pH range with measuring instruments capable of ±0.1 mV accuracy [12]. The accuracy attained to date has been

limited by the measuring instruments and reference electrodes rather than

the ion-selective electrodes. Stability and accuracy of about 0.01 mV

may be predicted from properly planned and interpreted ion-selective

electrode measurements. Meaningful interpretation of analytical information to 0. 1 percent relative error is then possible.
INDUSTRIAL ANALYSIS AND CONTROL 357

IV. Activity and Concentration

Analytical composition information may be desired either in terms of

the ionic activity, ai of Equation (1), or in terms of the analytical concentration, d, as determined by many classically used analytical chemistry

procedures. Either activity or concentration information may be obtained

from properly planned ion-selective measurement readings. The relation- ship between activity and concentration is given simply by:

ai==yiCi (5)

The single ion activity coefficient, y,, may be derived both theoretically

and empirically; in "real" chemical solutions, it usually differs significantly from unity. It is principally a function of the ionic strength of the

solution, /: 1= (1/2) ^Ciz\ (6)

Correlation of the single ion activity coefficient with the ionic strength of

a solution has been provided by the Debye-Huckel equation applicable to

dilute solutions:

Tabulated data for estimated single ion and mean ionic activity coeffi- cients in solutions of various ionic strengths are available [ 13,14]

.

In practice, more information is available for mean ion activity coeffi- cients than for single ion activity coefficients. Single ion activity coeffi- cients are not accessible to direct measurement and require adoption of a convention, such as the Debye-Huckel Equation (7). Single ion activity

coefficients, nevertheless, are needed for interpretation of ion-selective

electrode data derived from Equation (1). Since the standardization, interpretation and application of ion-selective electrodes depend on standard reference materials of known activity,

it is encouraging to note that Bates and coworkers of the National Bureau

of Standards have initiated studies dealing with the standardization of

ion-selective electrodes [15] and ionic activity scales [16]. A. Free and Total Ion Concentration

Ion-selective electrodes measure ionic activity, as shown in Equations

(1) and (2). The ionic activity is frequently less than the ionic concentration, the relationship being expressed by the activity coefficient of Equa-
358 ION-SELECTIVE ELECTRODES

tion (5). There is still another factor which may make the observed ion activity less than the total ion concentration. This is the tendency for ions in solution to associate with other ions to form undissociated molecules. Ex- amples of this are the formation of weak acids, weak bases, insoluble

precipitates and complex molecules or ions. For example, the weak acid,

HA, is slightly dissociated:

HA = H+ + A- (8) and obeys the following equilibrium expression:

Ka = ^^^^ (9) Aha

Using the activity coefficient concept introduced in Equation (5), the

equilibrium expression may be written in terms of the concentrations and

activity coefficients:

Tha^ha

and solved for the activity of the hydrogen ion,

«H+ =7h^Ch+ = 7^ Ka (11) \^A-yA-/

The Nernst equation for the glass pH electrode may then be written in terms of concentrations and activity coefficients:

E = E°+ (0.1984irM) log (^MlHA^I j^^ (12)

In practice. Equation (12) is difficult to use for interpretation of

ion-selective electrode emfs. Not only does it lack simplicity, but

frequently, data for activity coefficients and equilibrium constants are not

available for "real" solutions of varying ionic strength and unknown

quantities of impurities.

B. High Ionic Strength Medium

By introducing the concept of the high ionic strength medium, Equation

(12) may be simplified and made to be direct in terms of concentration.

The high ionic strength medium contains an inert electrolyte, not nor- mally present in the test solution, in large enough concentration to swamp
INDUSTRIAL ANALYSIS AND CONTROL 359

out the ionic strength contribution of the test solution itself. Equation ( 1 2)

may then be simplified for interpretation in terms of concentration:

£=£°'+ (0.19841 Tin) log Ch+. (13)

The constant, E^', of Equation (13) may be determined by calibrating

the ion-selective electrode cell with a standard solution of known concentration which has been suitably mixed with the high ionic strength medi- um. By treating the unknown solution in the same fashion as the standard, one calibration curve serves to determine the concentration of a given ion

in a solution regardless of the original environment of that ion. In some

cases, the high ionic strength medium may be refined to include a pH

buffer and complexing agents to eliminate the effect of interferences. An

excellent example is furnished by the medium called "TISAB" (Total

Ionic Strength Adjustment Buffer) [17], and used for directly measuring

the concentration of fluoride ion in public water supplies and many other

media. The composition of TISAB is given in Table 2. Table 2. Composition of *'TISAB", a high ionic strength

buffered complexing medium for measuring fluoride

ion concentration [Anal. Chem. 40, 1169 (1968)].

Sodium Chloride l.OM

Acetic Acid 0.25 M

Sodium Acetate 0.75 M

Sodium Citrate 0.001 M

pH 5.0

Ionic Strength 1.75M

In use, equal volumes of the sample and TISAB are mixed thus fixing

the ionic strength high enough to make the activity coefficients of un- knowns and standards virtually identical. The optimum pH range for the

fluoride electrode is at pH 5 and this is provided by the sodium

acetate-acetic acid buffer. Some citrate ion is added to preferentially complex metal ions such as iron and aluminum and insure that the fluoride ion

is displaced into the solution as "free" fluoride. V. Industrial Modes for Using Ion-Selective Electrodes

Industrial analytical instruments differ from laboratory instruments in that operation must be continuous without operator attention and that
360 ION-SELECTIVE ELECTRODES

more extreme sampling and environment conditions may be encountered.

Operations such as zeroing and standardization must be automatic and

maintenance should be minimal. The final signal emitted from the industrial analytical instrument must be a known function of the process composition and compatible with recording, controlling, and computing equip- ment.

Several methods of incorporating ion-selective electrodes in continuous

process analytical instruments may be devised. Figure 4 shows an

ion-selective electrode, M, and a reference electrode, R, monitoring a

ANALYTICAL CONTROLLER

STREAM B f » t><f

STREAM A

\ w

MEASURING ELECTRODE

TEMPERATURE

COMPENSATOR

Figure 4. Ion-selective electrode process control system. Stream by direct potentiometry in a flow-through cell. The process or sample stream is continuously flowing past the electrodes. The outputs of

the electrodes and the temperature compensator, 7, are fed into a converter which then permits continuous analytical recording, AR, and

controlling, AC, of the process stream. This system is applicable to streams in which the ion-selective electrodes encounter no interferences.

The monitoring of pH in a variety of process and waste monitoring

systems is well established.

The feasibility of monitoring ion exchange water purification units with

water hardness electrodes has been demonstrated [18]. A continuous

monitor for fluoride ion analysis in potable water supplies has also been

described [19]. Figure 5 illustrates the analysis of two water supplies,

with and without added fluoride, as performed by the continuous analysis

system and shows that 40 mV of ''signal" exists between the two concentration levels. Furthermore, this continuous analysis system makes use of
INDUSTRIAL ANALYSIS AND CONTROL 361

-40

+20-

+40-

PROVIDEN

1.05 CE T/ MG/L

<P V

ITER

/AT :R

FO)

0.18

\r\\ MG/

> \A/ W

LITE ATR

0.2 0.4 0.6 1.0 2.0 4.0 6.0 FLUORIDE MG / LITER

Figure 5. Fluoride in potable water supplies. the symmetrical cell principle [2 ] to achieve measurements independent

of the temperature at the iso-potential point of 1 mg F-/1. This reduction

of the temperature coefficient to virtually zero is illustrated in Figure 6

and is achieved by filling both the measuring and reference electrodes

with the same internal solution. A schematic drawing of the continuous

fluoride monitor is shown in Figure 7. The monitoring of the sulfide ion in the paper and pulp industry is another application of the direct monitoring system which is being studied. The digesting liquor of the Kraft pulping process is an alkaline mixture of sodium sulfide. At many points in the process stream, there exists a need for sulfide analysis information. At one stage in the process, the

spent black liquor is subjected to oxidation by air or oxygen to reduce sul- fur losses and minimize release of malodorous gases such as hydrogen

sulfide, mercaptans and methyl sulfides. Figure 8, based on laboratory

studies [20J, shows the monitoring of black liquor with both a sulfide and

an ORP (oxidation-reduction potential) platinum electrode while the solu- tion is being purged with oxygen to reduce the sulfide content. At the start of the oxidation, it can be learned from a suitable calibra- tion curve used in conjunction with Figure 8 that the sodium sulfide content is equivalent to 4 g Na2S/l (corresponding to — 8 10 mV).

This is reduced by 99.9 percent {i.e., three 30 mV decades) within a

half hour. Within the next half hour, the sulfide decreases substantially
362 ION-SELECTIVE ELECTRODES

EMF ( MILLIVOLTS)

Figure 6. Response of matched fluoride and reference electrodes as a function of temperature.

further by 12 more decades (360 mV), but at a different rate than the

reaction of the first half hour. The third half hour brings even more star- tling results in that the sulfide ion activity now increases as oxygen continues to bubble through the solution. Finally, in the fourth half hour, the
INDUSTRIAL ANALYSIS AND CONTROL 363

ELECTRONIC

RECORDER

FLUORIDE -TO

CURRENT

CONVERTER

FLOW-THROUGH

CHAMBER

WASTE

DISTRIBUTION

SYSTEM

Figure 7. Continuous monitoring of fluoride in potable water supplies. new supply of sulfide is also oxidized and the sulfide content is reduced to the "mud" level of the solution and the electrode, about —300 mV cor- responding to 10"^^ molar sulfide ion. Although studies are incomplete, it appears that the sulfide is present in two main forms. Inorganic sulfides,

such as sodium sulfide, which are 50 percent or more dissociated to "free" sulfide ion in the strongly alkaline (pH>12) black liquor, and or- ganic sulfides, such as the mercaptans and methyl sulfides, which are dis- sociated in only trace amounts, are both found in the black liquor. The in- organic sulfides are readily oxidized within the first half hour. The organic

sulfides are oxidized more slowly, with the rate of dissociation being the

limiting step of the reaction. The reappearance of sulfide has been noted

when one of the products of oxidation is elemental sulfur [21,22]. The
ORP electrode follows the oxidation procedure in a manner similar to the

sulfide electrode, but without the specificity to characterize the slope and

rate changes observed by the sulfide electrode.

Figure 9 illustrates multiple ion-selective electrodes. Ma, Mg, and Mc,

in a flow-through cell. Such an installation may be used for measuring

several constituents simultaneously, or for permitting a correction to be

made to an ion-selective electrode by a signal processor. For example, the

cyanide ion electrode measures only free cyanide ion which exists for

practical purposes only in alkaline solutions. If the cyanide ion electrode were to be used for monitoring pollution in a stream which might have

neutral or acid pH, the electrode reading could not be interpreted without

a knowledge of the pH. Introducing both the pH and cyanide ion elec- trodes and a signal processor for making the necessary pH correction

derived from Equations (8) through (12) would permit continuous monitoring of the total cyanide content of the stream. A computer solution for cation analysis using sodium and potassium electrodes has been reported

[23]. Figure 10 illustrates another possible method of compensating for the

ion-selective electrodes which are not completely selective to the ion
INDUSTRIAL ANALYSIS AND CONTROL 365

STREAM B

STREAM A

Figure 9. Multiple ion-selective electrodes process control system.

SAMPLE

STREAM

Figure 10. Ion-selective electrode system with reagent addition. whose measurement is desired. This system would permit reagent addition to the sample stream before it is measured by the ion-selective elec- trode. For example, pH is a constantly recurring limitation of ion-selective electrodes. Injection of a suitable buffer in a sufficiently small quantity so as to not significantly dilute the stream would extend the useful measuring range of many electrodes. Figure 10 illustrates a flow ratio con-
366 ION-SELECTIVE ELECTRODES

troller, FrC, used to control the ratio of reagent to sample, each of which

has been measured by passing through flow transmitters, FT. An application of the reagent addition system is afforded by looking again at fluoride

analysis in public water supplies. Figure 1 1 shows that direct potentiometry for fluoride determinations at the 1 mg/1 level is suitable in the

-40

Oh^~ of INTERFE ^ence/

HF FOf^MATIOr

0 -1

-30

-20 O

^-10

+10

+20

+30i

6pH

10

Figure 1 L Response of the fluoride electrode as a function of pH at the 1 mg F~/l level. pH range of 4 to 8.5 [24]. This range includes over 90% of the public

water suppHes of the United States. Above pH 8.5, the electrode also

responds to hydroxide ion. By using the reagent addition system in Figure

10 and a buffered reagent such as TISAB, the fluoride content of any

water regardless of its pH could be monitored. Thus plants employing

hydrofluoric acid would have a system for guarding against loss of this hazardous and corrosive reagent.

The reagent addition system in Figure 10 could also be used with gase- ous reagents. The sodium ion electrode has already been noted as not useful for direct monitoring of low levels of sodium in acid solutions. A

system for continuously monitoring the sodium level of high purity water

used in boilers has been reported using injection of gaseous ammonia to assure that the solution is alkaline when sodium ion is measured [25]. Figure 1 2 illustrates the use of ion-selective electrodes as end-point de- tectors in continuous titration analysis. Such a system would involve measurement of both the sample and reagent, as well as provide a sequencing
INDUSTRIAL ANALYSIS AND CONTROL 367

TO

PROCESS

VALVE AC

SAMPLE STREAM

SIGNAL PROCESSOR

WITH LOGIC nno

o o o o

o o o o

o o o o

o o o o

REAGENT

CO

REAGENT

Figure 12. Continuous process titrator, ion-selective electrode end-point detector.

logic to control sample and reagent addition, readout and drain cycles.

The inherent accuracy of a few tenths of a percent offered by the titration principle could be achieved with a system such as this. Also, the vast

literature and methodology of titrations that are already used in quality

control laboratories would become accessible to instrumentation.

Even though ion-selective electrodes are inherently devices for measuring ions in solution, Figure 1 3 shows how they could be adapted to monitoring gas streams. By scrubbing the gaseous constituents with a suitable

reagent and measuring the quantity of gas and of reagent solution with

flow transmitters, FT, and the concentration of the resulting solution with an ion-selective electrode, the quantity of the gas in the sample stream

could be monitored with the signal processor. A system like that in Figure

12 might be applied to the monitoring of gaseous pollutants with the aid of

ion-selective electrodes such as sulfide, cyanide and fluoride. The fluoride

ion electrode has been applied to monitoring of fluoride in air and stack

gas effluents such as are emitted from the environment of various industrial processes [26].

Ion-selective electrodes may even be applied to the analysis of ions for which ion-selective electrodes are not yet known. This is possible if the

desired ion can be found to enter into a reaction with an ion for which an

electrode exists. Such an application is shown in Figure 14 which in- volves the principle of differential analysis using reagent addition. If a
368 ION-SELECTIVE ELECTRODES

GAS , SAMPLE f 1 STREAM ^

REAGENT MS

SIGNAL PROCESSOR

o o o

o o o o o o

R s /

SCRUBBER

Figure 13. Continuous gas analyzer using ion-selective electrode.

REAGENT

STANDARD,

SOLUTIONVl

SAMPLE,

STREAM) FT

SIGNAL PROCESSOR

ION -SELECTIVE MEMBRANE

Figure 14. Differential cell with ion-selective membrane.

flow-through cell is constructed as shown in Figure 14 with two compartments separated by an ion-selective membrane, then a reagent stream

may be made to flow directly over the surface of the membrane in the
INDUSTRIAL ANALYSIS AND CONTROL 369

right hand compartment. The same reagent stream, measured by a flow

transmitter, FT, and mixed with the sample stream by a flow ratio controller, FrC, then flows past the second surface of the membrane.

The difference in activity between the two surfaces of the membrane

is measured as the difference in potential, AE, between the two reference

electrodes, R. Although similar in principle to the reagent addition

system of Figure 10, greater measurement precision ought to be attain- able because many minor errors, such as temperature drifting and changes

in reagent solution, would be self-canceling. In practice, this instrument

would be zeroed by permitting the reagent to flow past both membrane

surfaces and calibrated to full scale by use of a standard solution injected

as shown in Figure 14. An application of this differential analysis cell may be illustrated in con- nection with the problem of aluminum analysis [18]. An electrode selective for aluminum ion does not yet exist, but aluminum is known to form

a strong complex with fluoride:

AP+ + nF- = AlFw (14)

Table 3 shows some data obtained when small amounts of a standard

aluminum solution are added to a specially prepared high ionic strength

fluoride reagent solution buffered to pH 5. The composition of this re- agent is similar to that of the TISAB solution of Table 2, except that 0.0526M sodium fluoride is added and the citrate is omitted. The change

in emf, AE, upon the addition of aluminum solution to the fluoride reagent

Table 3. Addition of A V ml of 0.0945 M AICI3 to 100 ml of specially

buffered fluoride solution (see text). AV E AE y X K

(ml) (mV) (mV) (mr^) (mmoles Al) (mg Al)

0 -26.6

1 -23.6 3.0 1.124 0.1014 0.932 25.15

2 -20.2 6.4 1.283 0.1025 0.922 24.88

3 -16.4 10.2 1.487 0.1024 0.923 24.90

(Average) 0.926 25.0
370 ION-SELECTIVE ELECTRODES

may be correlated to the concentration of the aluminum by the following

equations:

C^^ = KX (15)

where ^

FaF

Y=\{)(^EIQ.\984\T)

K=^ (18)

From the data in Table 3, it is possible to show that fi, the fluoride to aluminum ratio, is 5.7 and this is sensibly constant over at least a 10 mV

span for AE. This differential analysis system has been applied in the

laboratory to the determination of aluminum in some simulated Bayer

liquor solutions, which are process fluids in the aluminum industries. The

principal ingredients of this liquor are sodium aluminate, sodium hydroxide and sodium carbonate.

Table 4 shows the results of several of these analyses and illustrates that relative errors of less than 4 percent for the analysis of aluminum may

be obtained if the emf data are accurate to the order of 0. 1 mV.

Table 4. Analysis of simulated Bayer liquor solutions containing

NaA102, NaOH and NagCOg.

Aluminum Aluminum Relative

Solution AV AE found theoretical error

(ml) (mV) (g/1) (g/1) (%)

1 1.00 3.1 2.62 2.65 -1.1

2 1.00 4.9 4.13 4.23 -2.4

3 1.00 4.5 3.82 3.83 -0.3

4 1.00 7.9 6.44 6.21 +3.70

The preceding discussion has shown that appHcations of ion-selective

electrodes to problems of industrial analysis are just emerging. A few of

the applications have already resulted in commercially available analytical instrumentation; many of them have had feasibility demonstrated, and
INDUSTRIAL ANALYSIS AND CONTROL 371

it may be anticipated they will be adopted as their significance becomes

appreciated and indeed as ion-selective electrodes themselves become ac- cepted as another modern tool required by analytical chemists to give

quantitative information accurately and efficiently.

Table 5 singles out approximately half of the commercially available

electrodes listed in Table 1 as having special promise for industrial and

Table 5. Suggested industrial and pollution monitoring applications of

ion—selective electrodes.

Electrode

designated for: Cadmium

Calcium and/or Water Hardness

Chloride

Cyanide

Cupric

Fluoride

Fluoroborate

Nitrate

Silver

Sodium

Possible application

Plating Solutions, Industrial Wastes

Boiler and Process Feedwater, Water Softening and

Ion Exchange Equipment, Water Treatment Plants

Water Brackishness, Desalination; Food,

Pharmaceutical, and other Industries

Liquid and Gaseous Waste Pollution Monitoring,

Cyanide Oxidation Systems, Plating and Rinse

Tanks, Metal Finishing and Extraction Processes

Plating and Rinse Tanks, Etching Baths for Printed Circuit Board Manufacture, Ore Extraction

Processes, Industrial and Mining Waste Water Potable Water Monitoring , Stream and Stack Gas

Effluents in Aluminum and Phosphate Ore

Industries, , Monitoring for Hydrofluoric Acid Leaks

in Industrial Processes

Plating Baths , Measurement of Boron Following

Conversion to Fluoroborate Water Supplies, Sewage

Photographic Industry —Emulsions and Fixing

Solutions

Food Industry, Natural, Brackish and Industrial

Process Waters, Break Through of Ion Exchange

Units

Sulfide Water, Stack Gas and Air Pollution Monitoring,

Paper Pulp and Petroleum Industry, Drilling Muds
372 ION-SELECTIVE ELECTRODES

pollution monitoring applications. Table 5 also lists some possible industrial and pollution monitoring applications of these electrodes. It is an- ticipated that this list will continue to grow within the next few years. Nomenclature

A constant of the Debye-Huckel equation

Gi activity of ion

B constant of the Debye-Hiickel equation

C, concentration of ion "/"

AC error in concentration

E emf of an electrode (in mV)

E° standard emf of an electrode (in mV)

AE change of emf of an electrode upon addition of aluminum solution; also used to denote error in electrode measurement (in

mV)

K, K' constant defined in Equation (18) and Table 3 Ka acid dissociation constant

Kij selectivity coefficient of ion with respect to ion

m an integer or fraction n an integer corresponding to the electron change in an elec- trode reaction n the ratio of fluoride to aluminum in the complex A\Fn

R E percent relative error in concentration

/ ionic strength of solution, defined in Equation (6)

T absolute temperature in °K

Vq volume of fluoride reagent solution (in ml)

A V volume of aluminum solution added (in ml)

X function defined in Equation ( 1 6)

Y function defined in Equation (17)

Zi charge on ion

7/ activity coefficient of ion

(d E/ d T) th thermal temperature coefficient of an electrode

( d E°l d 7) th standard thermal temperature coefficient of an electrode

Symbols Used in Figures

A alarm

AC analytical controller

AR analyfical recorder

FT flow transmitter

FrC flow ratio controller

M measuring electrode

MR combination measuring— reference electrode
INDUSTRIAL ANALYSIS AND CONTROL 373

R reference electrode

S solenoid valve

T temperature compensator

VI. References

[I] Light, T. S.. "Selective Ion Electrodes" in Analysis Instrumentation. Vol. 5, L. Fowler, R. G. Harmon and D. K. Roe, Eds., Plenum Press, New York, 1968, pp. 73-87.

[2] Bates, R. G., Determination of pH, Theory and Practice, John Wiley and Sons, New

York, 1964.

[3] Mattock, G., pH Measurement and Titration, The Macmillan Company, New York,

1961.

[4] Eisenman, G., Ed., Glass Electrodes for Hydrogen and Other Cations, Marcel

Dekker, Inc., New York, 1 967.

[5] Eisenman, G., Bates, R. G., Mattock, G., and Friedman, S. M.,The Glass Electrode,

Interscience Publishers, Div. of John Wiley and Sons, New York, 1 966.

[6] Frant, M. S.,and Ross, J. W., Jr., Canadian Patent 763082, July 11, 1967.

[7] Light, T. S.,andSwartz,J. L., Anal. Lett. 1,825 (1968).

[8] Ross,J.W., Science 156, 1378(1967).

[9] Moore, E. W., and Wilson, D. W., J. Clin. Invest. 42, 293 ( 1 963).

[ 10] deBethune, A. J., Light, T. S., and Swendeman, N., J. Electrochem. Soc. 106, 616

(1959); also in Encyclopedia of Electrochemistry, C. A. Hampel, Ed., Reinhold,

New York, 1 964, pp. 4 1 2-434.

[1 1] Bates, R. G., J. Res. Nat. Bur. Stand. 66A, 179(1962).

[ 1 2] Light, T. S., and Fletcher, K., 1 1 1 , Anal. Chem. 39, 70 ( 1 967).

[ 13] Harned, H. S., and Owen, B. B., The Physical Chemistry of Electrolyte Solutions, Reinhold, New York, 1958. [14] Meites, L., Ed., Handbook of Analytical Chemistry, McGraw-Hill, New York,

1963, pp. 1-6 to 1-13. [15] Bates, R. G., Ed., Electrochemical Analysis Section: Summary of Activities July

1 967 to June 1 968, Technical Note 453, U. S. Department of Commerce, National Bureau of Standards, July 1968, pp. 37-45.

[16] Alfenaar, M., and Bates, R. G., "Scales of Ionic Activity and Standards of

Ion-Specific Electrodes", paper presented at 156th American Chemical Society National Meeting, Atlantic City, Sept. 8-13, 1968.

[ 1 7] Frant, M.S., and Ross, J. W., Jr., Anal. Chem. 40, I 1 69 ( 1 968).

[ 1 8] Light, T. S., and Mannion, R. F., unpublished results. [19] Babcock, R. H., and Johnson, K. A., J. Amer. Waterworks Assoc. 60, 953 (1968). [20] Light, T. S., and Swartz, J. L., unpublished results. [21] Chen, K. Y., and Morris, J. C, "Oxidation of Sulfide by Aqueous O/', paper

presented at the First Northeast Regional Meeting, American Chemical Society, Boston, Mass., Oct. 13-15, 1968. [22] Murray, F. E., TAPPI 42, 9 (1959). [23] Friedman, S. M..and Bowers, F. K., Anal. Biochem. 5, 47 1 (1963). [24] Light, T. S., "Analytical Evaluation of the Fluoride Ion Electrode", paper presented

at the Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy. Mar. 5-10, 1967.
374 ION-SELECTIVE ELECTRODES

[25] Diggens, A. A., "Determination of Low Levels of Sodium in Water with a Sodium

Responsive Electrode", paper presented at Symposium on Automatic Analytical

Systems in Water Analysis. Soc. for Anal. Chem., London. Nov. 1 7. 1 967.

[26] Elfers, L. A., and Decker, C. E., Anal. Chem. 40, 1658(1968).
CHAPTER n

ANALYTICAL TECHNIQUES

AND APPLICATIONS OF

ION-SELECTIVE ELECTRODES

Richard A. Durst

Institute for Materials Research

National Bureau of Standards

Washington, D.C. 20234

I. Introduction

The present analytical applications of ion-selective electrodes are many

and varied, and certainly as new types of electrodes are developed, the list of uses will grow at an increasing rate. In general, the analytical

techniques will fall into one of two classes; direct potentiometric measurements based on the Nernstian logarithmic relationship between emf

and ionic activity, and potentiometric titrations which, when applicable, are usually more accurate and precise.

Although the analytical usefulness of these electrodes has already been

presented for a number of systems, such a? in the studies of complexes

and reaction kinetics, for process and quality control, and in biomedical

studies, this section will compliment these discussions by presenting ap- plications to the more usual types of laboratory analyses. At present,

these applications include studies on more than a dozen ionic species in fields ranging from the usual chemical research and development to diverse studies in agriculture, geology, oceanography, and water and air pollution.

II. Direct Potentiometry A. The Nernst Equation

An analytical determination based upon the application of the Nernst

equation is experimentally very simple. It merely involves the measure- ment of the emf of a cell consisting of an electrode selective to the ion of

interest and a suitable reference electrode, the potential of which is accurately known and stable. The Nernst equation is then solved for the activity of the analate species using the observed cell emf. Unfortunately,

however, the interpretation of the measured emf is usually quite difficult,

since the cell potential which is measured also includes a liquid junction

375
376 ION-SELECTIVE ELECTRODES

potential term, £j, that is, Ecell = Eind — Ej-ef-^ Ej (1)

where Ejnd and Eref are the potentials of the ion-selective indicator and

reference electrodes, respectively. For an ion-selective electrode

responding, for example, to some univalent anion, X", we have

^cell = EVna-y^ In ax- - ^ref + Ej (2) and

ttx-^antilog^-y^g^ (-£'eell + £'°nd-^ref + £'j) (3) where T is the temperature in kelvins, and the various potential terms are

in millivolts. It should also be noted that the E°^^ is not the "standard

potential" of the indicator electrode in the usual sense. Instead, it more

closely resembles the "zero potential" of the glass pH electrode which in- cludes the contributions from the inner reference electrode, the inner

phase boundary potential of the membrane, and the asymmetry potential.

The value of E^nd must therefore be evaluated for each electrode before Equation (3) can be applied.

Another disadvantage of the direct evaluation of the Nernst equation

derives from the fact that the results are in terms of ionic activity. Since

concentration is the usual quantity of interest in analyses, it is necessary

to have activity coefficient data available to convert activity to concentration. For mixed electrolyte systems, these data are seldom, if ever,

available. From Equation (3), it is easily calculated that an error of one millivolt

in any of the potential terms corresponds to an error of approximately 4%

in flx-- For a divalent ion, the response slope, mV/pX=, is one-half that of a univalent ion, and the error increases to about 8%/mV.

Thus the uncertainty in Ej, and the activity coefficients plus

the difficulty in measuring the Eceii to better than ±0.1 mV, all combine

to limit the precision of the direct technique based on the evaluation of the

Nernst equation to about ± 0.5%.

B. Concentration Cell Techniques

One method of avoiding some of the above difficulties is to employ a concentration cell technique. The null-point technique, first performed by

deBrouckere in 1 928 [ 1 ] , was refined by Malmstadt and coworkers [2-5]

in the late fifties and early sixties. In principle, null-point potentiometry

is a simple concentration cell technique that compares the solution to be

analyzed (analate solution) with a solution of known composition. The
ANALYTICAL TECHNIQUES AND APPLICATIONS 377

usual procedure consists of adjusting the composition of one of the

half-cell solutions to match the other as evidenced by zero cell potential

when measured between identical indicator electrodes specific for the

species being determined.

For the general case of a concentration cell of this type, the emf is given

by

where C and y are the concentration and activity coefficient, respectively,

of the species being determined, and the subscripts 1 and 2 indicate the

analate and variable known solutions. If a sufficiently large excess of an

inert electrolyte is used in both half cells, Ej will become negligible since

it depends on the difference in the electrolyte concentration between the

two half cells. Also, the activity coefficients of the ionic species in the two

half cells will be approximately equal due to the constant high ionic

strength maintained by the inert electrolyte.

Equation (4) then simplifies to ^

59.16 , Ci

At Lv 2 That is, when both half cells are at the same temperature (usually 298K),

the cell emf is dependent only on the concentration ratio of

electrode-selective species. From Equation (5), when Eceii 0^ the analate

concentration, Ci, is equal to the known concentration, Cz. If the concentration in the variable known half cell is varied volumetrically, i.e., by

dilution with the inert electrolyte solution or by addition of a concentrated

solution of the electrode-selective species [6], as opposed to coulometric

generation of the species in situ [7] , then the usual dilution correction fac- tor must be applied to calculate the known concentration, Cz. The null-point technique can be applied in two ways: 1) as a "dead-stop" method, or 2) as a linear interpolation "titration" technique.

In the dead-stop method, diluent or a standard solution of the species of

interest is added until the null point is reached, and the analate concentration is evaluated from the known concentration in the variable half cell. In

the linear null-point potentiometric technique, aliquots of the diluent or standard solution are added incrementally, and emf measurements are made prior to and after the null point. These emf data are then plotted

semi-logarithmically {Eceu vs. log C-z) resulting in a "linear titration curve"

with a slope of 59/^? millivolts per decade change in concentration and an

intercept at Epeu = 0 where Cz = Ci. Computer techniques have been ap- plied to the data evaluation for this method whereby the intercept

(end-point concentration) of the linear least squares fit of the data is
378 ION-SELECTIVE ELECTRODES

printed out along with the slope of the titration curve (which serves as a check on the electrode behavior).

The null-point technique easily lends itself to the analysis of very small

volumes of solution. At the National Bureau of Standards, this technique

has been used for the determination of fluoride [6] and silver [7] in volumes ranging from 5 to 100 /itl. Using the concentration cell arrange- ment in Figure 1, 0.380 nanograms of fluoride were determined in a sample volume of 10 /Ltl with an error of only 0.002 ng. Over the range 0.38 to 190 ng, fluoride was determined with an average error of about 1%. In the case of silver, it was possible to determine 0.054 /xg in a volume of 100 /jlI with an error of 0.001 jjig [8], while over tne range 0.054 to 54 /xg, the

LEAD

ANALATE TITRATION

HALF CELL HALF CELL

Figure \. Concentration cell used for the determination of fluoride by linear null-point potentiometry.
ANALYTICAL TECHNIQUES AND APPLICATIONS 379

average error was less than 1%. In addition to its intrinsic simplicity, this technique has the additional advantages that the actual "titration" can be

performed in any convenient volume of solution, e.g., 100 ml as used in the NBS investigations, while the sub-ml volume of test solution is unchanged, i.e., it serves only as a reference and is not modified or chemically reacted during the determination, and can therefore be recovered for use in subsequent studies.

C. Calibration Curves

A commonly used method for directly relating the electrode potential

to the species activity or concentration is to construct an empirical

calibration curve. The data are usually plotted on semi-logarithmic graph

paper (Eceii vs. log at) which results in a linear calibration with a slope de- pendent on the ionic charge and electrode behavior. Basically, this can be

done in two ways. One method employs pure solutions of some completely dissociated salt of the species of interest covering the range of concentration being studied. In this case, the presence of indifferent electrolytes,

which are not true interferences in the usual sense of the word, will cause

errors due to their effect on the activity coefficient of the ion under in- vestigation through variations in the ionic strength of the system. For simple systems where activity coefficient data are available, corrections for

ionic strength effects can be easily made in order to relate the observed

cell potential and the activity or concentration of the species.

For more complex systems, it is necessary to use calibration solutions

which either approximate the background of the test solutions or contain an excess of an inert electrolyte (plus non-electrolytes, buffers, etc.) which will swamp out interferences and variations in the test solution

background. These two methods are equivalent to constructing a calibra- tion curve of "formal potentials" which include the effects due to activity,

liquid junction potentials and any background species which influence the

cell emf.

The choice of which of these two alternate calibration methods is used

depends primarily on the system itself. In cases where the background

concentration of the test solution is high, such as in sea water and most

biological systems, it would be very difficult to effectively swamp out the

background, and a series of calibration solutions with backgrounds ap- proximating that of the test solution would be required. However, very

often the technique of standard additions will be of value in systems of

this kind especially when the background is itself difficult to analyze or is variable. This technique is discussed in Section E below.

For less complex systems or for systems where it is desired to hold the

activity coefficient relatively constant to relate emf and concentration
380 ION-SELECTIVE ELECTRODES

more easily, an excess of an inert electrolyte or buffer solution will usually suffice. An important practical example of this method is demonstrated by the use of a total ionic strength adjustment buffer (TISAB) for the determination of fluoride in public water supplies [9]. This technique

is based on a 1:1 dilution of both standards and samples with the TISAB

solution (containing glacial acetic acid, sodium chloride, and sodium

citrate with its pH adjusted to 5.0-5.5 using sodium hydroxide) which

simultaneously performs three functions; 1) the ionic strength is fixed by

the high level of ions contained in the TISAB, 2) the solution is buffered

in a range where hydroxide does not interfere, and 3) any Fe^+ or AP+

present is complexed by the citrate thereby releasing bound fluoride. This

technique eliminates virtually all of the effects due to the background

variations of. water supplies, and makes possible the use of a single

calibration curve for a wide range of water samples. In addition to public

water supplies, this method should find application to the determination

of low levels of fluoride in a wide variety of aqueous systems, such as fluoride in urine or from scrubbers in air pollution monitors.

D. Electrode Cali iration

A technique closely related to the calibration curve methods depends on calibrating the electrode with one or more standard solutions and as- suming a linear emf vs. In(activity) relationship. This is essentially the same technique used in making pH measurements, and the activity of the

unknown is defined in terms of the emf difference between the unknown

and standard solutions (see Chapter 6). The use of two standard solutions which bracket the unknown solution

concentration increases the reliability of the method by establishing both

the "zero potential", E°', for the electrode system and the response slope.

This procedure will allow for most non-theoretical response characteristics of the electrode. The application of these calibration procedures

to direct potentiometric determinations is facilitated by the use of a pH-type meter which is provided with a logarithmic readout of the cell potential corresponding to the ion activity or concentration. The conventional pH meter will suffice for the direct readout of monovalent

cation-selective electrodes, i.e., the alkali metals and silver, but for monovalent anions and divalent cations and anions a special type of meter

is required. For the monovalent anions, a simple polarity-reversal switch on the pH meter would be sufficient (or reversal of the pH scale). For

divalent ions, a newer type of meter (Orion Series 400) is needed in which

provision is made for a Nernst factor of RTjlF in relating the cell emf to ionic activity or concentration. Here again, a provision for polarity reversal is required to permit readings on both divalent cations and anions. In
ANALYTICAL TECHNIQUES AND APPLICATIONS 381

addition, a temperature compensating adjustment and/or a slope-modifier

is needed to correct for the effect of temperature on the slope and to compensate for any deviation of the electrode response from the theoretical

Nernst slope. Using appropriate calibrating solutions, a meter of this type can be made direct reading in various concentration terms, such as parts

per million, molarity, normality, etc., and can also be used in making

water hardness measurements by again using the slope modifier to make

the proper proportionality adjustments for direct readout.

The use of this type of meter simplifies ion-selective electrode deter- minations in much the same way as the measurement of pH has been

facilitated by the use of pH meters. The time required for construcfing

calibration curves is saved in addition to the convenience of direct

readout in remote or on-stream continuous measurements. However,

whereas the glass pH electrode is more consistently Nernstian in its response, some of the ion-selective electrodes tend to be slightly less Nernstian, with response slopes as much as 2 or 3 millivolts less than

theoretical. This necessitates, for the time being at least, the use of the

bracketing method of calibration where the appropriate slope correction can be applied for direct readout. Except for a very slight decrease in sensitivity and precision, this effect is a relatively minor difficulty. It has also

been shown in several studies that once the response of one of these

electrodes is determined, it remains relatively stable so that only a

periodic check of the "zero potential" using a single reference solution

is necessary.

E. Addition Techniques

The standard addition technique, also called a "spike" or "known-increment" technique, is a very convenient method for the determination of

the total concentration of a species in very complex systems. This

technique avoids many of the difficulties usually encountered in solutions

with backgrounds containing high concentrations of other ions or complexing agents. In order to apply this technique, the only preliminary requirement is a knowledge of the electrode response to the species of interest. This

response is evaluated with standard soludons and should be determined

to as high a degree of precision as possible since the reliability of the

results will be no better than this value. Once evaluated, this response

slope or Nernst factor is usually quite stable and needs only periodic

rechecking. The usual standard addition procedure involves the addition

of one or more aliquots of the species of interest to the unknown sample

solution, being careful that the increment does not significantly change

the ionic strength of the system. Under these conditions, the activity coefficient (and liquid junction) can be assumed to remain constant, and the
382 ION-SELECTIVE ELECTRODES

observed emf change can be related through the Nernst equation to the

original unknown concentration (rather than activity).

The observed initial potential of the unknown sample solution as given

by the Nernst equation is:E, = E°'^^\nQ,y^ + Ej (6)

where Cx and 7x are the concentration and activity coefficient of the test ion, respectively, and the other terms retain their previous definitions. On

the addition of a known amount of the test ion, a new potential is measured:

£2 = ^°'+^ln (Cx + AC)yx+^j (7) nr where AC is the increase in concentration of the test ion produced by the

standard addition. Since the addition is made in such a way that the ionic

strength and nature of the system are virtually unchanged, then E°', Ej,

and the activity coefficient should remain unchanged by the addition of

the spike. On taking the difference between the initial and final potentials,

the "constant" terms E°', Ej, and y{i.e., 7x = 7x) cancel out, and we

have

AE = E..-E. = -ln[-^) (8)

Rearranging, and substituting S for the Nernst slope, 2.3 RT/nF, which

is experimentally confirmed by a series of known standard solutions

covering the concentration range of interest, Equation (8) becomes:

AE ^ /Cx + AC\

and, taking antilogarithms and solving for the concentration of the original

test solution:

Cx==AC(10^^/^-l)-i (10)

or, related back to the actual concentration of the standard addition solution:

where Cs is the standard solution concentration, Vs is the volume of the

standard addition aliquot, and Vx is the test solution volume. Equation

(11) was derived assuming the volume of the standard solution, Vs, is
ANALYTICAL TECHNIQUES AND APPLICATIONS 383

negligible in comparison to the original test solution volume, Fx. If this as- sumption does not hold, the most general form of the standard addition

equation becomes:

which takes into consideration the changes in concentration of both the

standard solution and the original test solution.

From Equation (12), it is seen that the precision to which Cx can be

determined directly depends on the reliability to which Cs, Vs, Vx, S,

and are known. The standard solution concentration, Cs, and the test solution and standard addition volumes can normally be prepared and/or

measured quite accurately and should not limit the precision of the

method. Similarly, the Nernst slope, S, can usually be determined with a

relatively high degree of precision. In most cases, it will be the emf measurements. El and E2, which will cause the most difficulty. Also, the rela- tive uncertainty of these measurements will become more significant the

smaller the value of AE. This uncertainty can be reduced by making HE

as large as possible, but the addition must not be so large as to affect the

ionic strength of the solution, as discussed above. Thus, the optimum

results are obtained by balancing the increased reliability in the measure- ment of A£ by adding a large increment against possible variations in the

activity coefficient and liquid junction potential caused by changes in the

ionic strength. In the presence of excess complexing agents, the standard addition

technique is the only procedure available for determining the total concentration of the complexed species using ion-selective electrodes. This

method works because the added species is complexed to the same degree

as the test species, thus each emf measurement detects a constant fraction

of the total concentration. Again, this constant factor cancels out when

the difference emf, AE, is evaluated.

The standard addition procedure is further simplified by using a special

scale, unique, at the present time, to the Orion Model 407 meter. This

scale indicates the ratio of the amount of ion in the original solution to the

amount of ion added in the known increment. It is therefore unnecessary

to evaluate equations, such as Equations (10) and (11), with the possible

introduction of computational errors. The standard addition technique has been used in the determination of

trace fluoride [10]. Determinations were made in the concentration range

from 10""* to \0~^M fluoride in a variety of solutions without prior separation. Sample solutions of 50 ml were analyzed using 10-100 ix\ increments

of a 0.1 M sodium fluoride solution. Individual additions produced emf

(12)
384 ION-SELECTIVE ELECTRODES

changes of about 10 mV and were continued until a total change of at least 40 mV was achieved. Less than 1 ml of the standard solution is required for this emf change. The calculation of fluoride concentration was performed in two ways: 1) by a linear least squares fit to Equation (9) of 5 to 10 data points with both the slope and unknown concentration

computed, and 2) by calculating the unknown concentration from a single

known increment sufficiently large to produce an emf change of at least 40 mV and using a previously determined value for the slope. Over the

10~^ to 10~^M concentration range, the relative error of the technique was

about 10% and the relative standard deviation less than 5%.

In a brief study of the fluoride concentration in sea water [11], direct

emf measurements indicated a fluoride level of about 0.6 ppm, while the

standard addition technique gave a value of 1.2-1.3 ppm. These results in- dicate that approximately half of the fluoride in sea water is complexed by

the magnesium present. Of course, it should be pointed out that in many

types of determinations, such as ionic species in biologic media, it is the

activity of the free uncomplexed ions that is of interest, and in such cases, the standard addition technique could not be used unless the fraction

complexed were known.

The inverse technique of standard additions, called "analate additions

potentiometry" [12], is based on the addition of increments of the un- known (analate) solution to a known volume of a standard solution of the same species. The change in emf is then related to the unknown concentration by means of the Nernst equation as in the standard addition

technique. Equation (13) is derived by the simultaneous solution of the

Nernst equation for the change in emf produced by delivery of an aliquot

of the analate solution into the standard, and rearranged for evaluation of

the unknown concentration, Cxi

where all of the symbols retain their previous definitions. If the substitution N = {Vs-\- Kx)/Kx is made. Equation (13) more simply becomes:

Again, the only assumptions involved in the derivation of Equations (13)

and (14) are the constancy of the activity coefficient and the liquid junction potential. However, in this case, the ionic strength is controlled by

the background inert electrolyte of the standard solution.

The singular advantage of this technique over standard additions lies in the fact that the minimum volume requirement for electrode immersion is

(13)

c^=Cs[N- iO'^^/^-(yv-i)] (14)
ANALYTICAL TECHNIQUES AND APPLICATIONS 385

satisfied by the standard solution so that the increment of unknown solu- tion need only be as large as necessary to produce a useable emf response.

This analate volume requirement decreases as the volume and concentration of the standard solution is reduced. The standard solution concentration, however, is limited to the range where the response slope is greatest

and reproducible. The method suffers from the disadvantage that the solu- tion background does not correspond to the unknown solution

background but to that of the standard, and changes in the degree of complexation (if present) could introduce error. In general, the same limita- tions and uncertainties of measurement, e.g., emf, volumes, S, etc., apply

to this technique, and aside from its use as a microtechnique, the two

methods are otherwise comparable. This technique has been successfully

applied to the determination of fluoride in solutions containing elec- trochemically generated fluoride ion [13]. The precision of the technique

at the millimolar concentration level is about 0.5% (95% confidence

limits). In summary, the method of standard additions is recommended as the

first-choice technique with analate additions used only in cases where the

volume of unknown is severely limited or where it is desired to avoid dilu- tion of a concentrated test solution.

The above sections briefly summarize the direct potentiometric

techniques available for use with ion-selective electrodes. In general, they

offer a means of rapid analysis and can be applied to an almost unlimited

variety of systems. The technique of choice, obviously, will depend on the nature of the system of interest.

III. Potentiometric Titrations In contrast to the direct potentiometric methods based on the Nernst

equation, potentiometric titrations generally offer an increase in accuracy

and precision at the cost of increased time and difficulty. The increase in accuracy comes about for two main reasons: 1) measured potentials are used to detect rapid changes in concentration (activity) that occur at the

equivalence point of the titration and this rate of emf change is usually

considerably greater than the response slope which limits precision in direct potentiometry, and 2) since it is the change in emf {vs. the volume

of a standard reagent) rather than the absolute value of the emf which is of interest, the influences of liquid junction potentials and activity coeffi- cients have little or no effect. The accuracy of these titrations is primarily

determined by the accuracy of standardization and volume measurement

of the titrant and by the sharpness of the potential "break" at the end

point (as determined by the equilibrium constant of the titration reaction).

Titration techniques are widely applicable and can be based on a variety of reactions: neutralization (acid-base), precipitation, redox, and
386 ION-SELECTIVE ELECTRODES

complexation. In addition, the titration reaction must be stoichiometric,

relatively fast, and must go to completion.

The critical problem in a titration, of course, is to identify the point at which the reacting species are present in equivalent amounts. This

equivalence point either exactly or virtually coincides with the inflection

point of a plot of the cell emf vs. the volume of reagent added. In the case

of non-1 :1 reactions, this can be easily reaHzed by standardizing the

titrant against a known amount of the analate using the same titration procedure and arbitrarily designating the inflection point of the unsymmetrical titration curve as the equivalence point.

The equivalence point of a typical sigmoid titration curve can be

located in two ways: 1) the equivalence-point emf can be calculated or measured beforehand using standards and then the volume of reagent

required to reach that potential is found, or 2) the inflection point can be

located graphically.

Titration to the equivalence-point potential is exactly analogous to ordi- nary indicator titrations, and. since recording the data is unnecessary, it is convenient and rapid. The precision of this simple method depends on

the reproducibility of the equivalence-point potential, but because of the

normally steep slope of the emf-volume curve near the equivalence point, a knowledge of this potential to 10 mV usually results in sufficiently

high precision.

The most obvious graphical method for locating the equivalence point

is by inspection of the emf vs. volume titration curve to find the point of

maximum slope (Fig. 2a). With this method, relatively large aliquots of

the titrant are added until the equivalence point is approached, where the

increments are reduced until the equivalence point is passed. After each

increment sufficient time is allowed for the system to reach equilibrium.

Often, this is most easily done using a recorder to display the emf vs. time.

Constructing the curve and locating the point of maximum slope may in- troduce error due to personal judgment.

The equivalence point can usually be located more conveniently and

accurately by adding small, equal-volume increments of the titrant in the

vicinity of the equivalence point and evaluating the equivalence point

from the first or second derivative curves of the titration data (Figs. 2b

and 2c). In the case of the first derivative, the point where the slope of the

data, AElAV, is a maximum corresponds to the equivalence point.

Another method, using second derivative data, calculates the equivalence

point from the point where \-EllV- becomes zero, i.e., corresponding to the maximum of the first derivative. This latter method does not require

graphical evaluation but is readily calculated using procedures outlined in most basic analytical textbooks. Since the equivalence point is computed

without the need of plotting and interpreting a graph, this method is less prone to the personal error cited above.
ANALYTICAL TECHNIQUES AND APPLICATIONS 387

One final method of evaluating titration data^ which has received little attention, is based on plotting AK/AE vs. titrant volume [14]. Although

somewhat less convenient to calculate than its reciprocal, AE/AK, since

the values of AE will not be uniform integers, certain advantages are obtained by this method. For a typical plot of this type (Fig. 2d), it is seen

that in the vicinity of the equivalence point, the curves consist of two

straight lines which intersect each other and the volume axis (according

to Gran [14]) at the equivalence point. Under some conditions, a deviation from the straight lines occurs just at the equivalence point. However,

if the straight portions are extrapolated, they will intersect at the volume

axis. Also, the slopes of the lines are indicative of the charges of the react- ing ions, i.e., for ions of the same charge, the lines are symmetrical about

the equivalence point, while for ions of different charges, the slopes will
388 ION-SELECTIVE ELECTRODES

differ. This technique is equally applicable to neutralization, precipitation,

complexation, and redox titrations. The high accuracy and precision of potentiometric titrations are widely

accepted. Since the equivalence point volume is independent of Ej, E°,

and Eref, the titration methods are also generally useable in non-aqueous

systems, where, except for matched concentration cell measurements,

direct potentiometric data are difficult to evaluate. Except for speed and

the application to very dilute solutions, the only distinct advantage of

direct potentiometry over potentiometric titrations is for the continuous

monitoring of changing systems where high accuracy is not essential. One additional advantage of potentiometric titrations over direct potentiometry that deserves mention is the possibility of using the selective ion

as the titrant in the determination of other species for which ion-selective

electrodes are not available. This simple device greatly extends the use- fulness of ion-selective electrodes to many other ions of interest. A case in point which provides an excellent example of this is the deter- mination of lithium by titration with fluoride [15]. This method was

developed for the analysis of concentrated LiCl and LiNO.} solutions

used in the Tramex process for the separation of lanthanides from acti- nides. The analytical technique utilizes the quantitative precipitation of

LiF in alcohol as the basis for the potentiometric titration with the

fluoride electrode. No bias existed between the fluoride titration results and those obtained by an ion exchange procedure in which the acid dis- placed from an acid-form cation exchange resin is titrated. The two

methods generally agreed to within 1%. The precision of the method for solutions approximately 1 IM in LiCl was 0.4% (relative standard deviation) and 0.3% for 0.085M LiCl. Figure 3 shows the effect of NaCl on the

shape of the LiCl titration curve. Sodium causes less than 3% error when

present in amounts up to 50 mole percent of the lithium. It is expected

that other alkali metals would interfere less than sodium. Interferences by

free acid and certain other metal ions can be eliminated by adding

NH4OH and (NH4j2S, respectively.

The above discussions of direct potentiometry and potentiometric titra- tions have of necessity been highly general in nature and were by no means intended as rigorous treatments. For this reason, exceptions to various points will occur, and discretion on the part of the analyst is necessary in the selection of the most suitable technique for a particular

problem.

IV. Applications

The past several years have seen a rapid increase in the use of

ion-selective electrodes in widely divergent disciplines. In fact, since the

first paper concerned with the present generation of commercial.
ANALYTICAL TECHNIQUES AND APPLICATIONS 389

VOLUME, NH^F TITRANT

Figure 3. Titration curves of lithium and sodium chlorides in ethyl alcohol with ammoni- um fluoride, a) LiCl only; b) NaCl only; c) LiCl + NaCl (Na+/Li+ ~ 0.5). From E. W. Baumann [15]. non-glass types of ion-selective electrodes appeared in 1965, the yearly

rate of publication has increased exponentially. In addition to the applications of these electrodes already discussed in the preceding sections,

selected applications illustrating various techniques and sample systems

will be described in this section. A bibliography of additional references

is given in an addendum to this chapter.

A number of general papers have appeared which have briefly surveyed

all or a part of the development and applications of these newer types of

ion-selective electrodes. Since even the most recent of these reviews is al- ready outdated by the latest developments, instead of discussing them in- dividually they are merely listed chronologically in the addendum.

A. Fluoride

Of all the ion-selective electrodes developed in recent years, the

fluoride electrode has probably been the most outstanding for two
390 ION-SELECTIVE ELECTRODES

reasons: 1) the importance of fluoride in commerce and technology, and

2) the difficulty in determining fluoride by previous techniques. Some

feeling for the importance of a rapid and reliable method for monitoring

fluoride can be gained by considering a list of materials in which fluoride occurs: 1) public water supplies (fluoridation), 2) pharmaceuticals {e.g.,

vitamins), 3) consumer products (toothpaste), 4) water and air (pollution

by discharge of industrial wastes), 5) soils (ecological effects of fluoride),

6) electroplating, cleaning, etching, and pickling baths (continuous monitoring for fluoride level regulation), 7) manufactured materials {e.g., fertil- izers, pesticides, glass, etc.), and 8) biological materials (present in tooth enamel, bone, urine, and plant materials).

Obviously, only a few of these varied applications can be presented

here, especially since the methods that have been developed are almost as numerous as the materials themselves. A general paper on the direct

potentiometric determination of fluoride [16] describes the working

characteristics of the electrode and the influence of foreign substances, in- cluding non-electrolytes, on the observed emf. The use of the standard addition technique and a novel form of the equation used to calculate

results are also discussed.

Lingane has published two important papers [17,18] on the titration of

fluoride with lanthanum, thorium, and calcium. In the first study, comparing the three titrant species, lanthanum was found to be the best titrant in neutral, unbuffered solution based on the titration curve slope at the

equivalence point as shown in Figure 4. Although the thorium titrant produced the greatest overall change in emf, it was more drawn out than

the lanthanum titration in the vicinity of the equivalence point, while cal- cium showed no inflection at all in unbuffered aqueous solution. In addition, the equivalence point potential is independent of fluoride sample size when titrated with lanthanum, but varies significantly in the thorium titra- tion. This is an important consideration if a manual or automatic titration to the equivalence-point potential is used as the analysis technique.

Since the fluoride-lanthanum titration is a 3:1 reaction, the titration curve is not symmetrical, and the point of maximum slope does not cor- respond to the true equivalence point (assuming so will result in a negative error). Using fluoride standards, the equivalence-point potential can be determined, or the titrant can be standardized in such a way that the

point of maximum slope does coincide with the true equivalence point.

Further studies [ 1 8] of the lanthanum titration in 60 to 70 volume percent

ethanol solution showed a considerable improvement in the titration curve, i.e., the slope at the equivalence point is increased (see Fig. 5)

because of the decrease in the solubility of lanthanum fluoride. Proceeding to some applications to specific analysis problems, the use

of the fluoride-selective electrode in the determination of fluoride in
ANALYTICAL TECHNIQUES AND APPLICATIONS 391

toothpastes has been reported by Shane and Miele[19]. Previously, the

determination of fluoride in toothpaste required a steam distillation separation step ordinarily followed by titration with thorium nitrate using a colored dye indicator. In the fluoride electrode procedure, no separations are required. The fluoride concentration at the 0.1% level (equivalent to 0.22% sodium fluoride or 0.4% stannous fluoride) was measured using a direct potentiometric method. The ionic fluoride content in an aqueous dispersion of toothpaste was determined by relating the observed emf to a semi-logarithmic calibration curve constructed by adding

known amounts of fluoride to a blank toothpaste formulation. The calibra- tion curve is linear in the range of interest, i.e., between 0.18 and 0.25%

NaF. The potentiometric technique is simpler and more rapid (5-9 min vs. 40-45 min) than the distillation-thorium titration method and gives results which indicate no significant difference between the two methods.

Another direct potentiometric technique has been used for the deter- mination of fluoride in bone [20]. The procedure consisted of ashing the
392 ION-SELECTIVE ELECTRODES

E

Figure 5. Titration of fluoride with lanthanum in neutral, unbuffered solution — influence of ethanol. a) Aqueous; b) 70% ethanol. From J. J. Lingane [18]. bone samples at 500 °C, dissolving the ash in HCl, nearly neutralizing

the excess HCl with NaOH, adjusting the final pH to 4.7 with sodium

acetate, and diluting to volume (5 ml). This procedure produced essentially the same ionic strength and pH in both the bone and standard solutions. A linear calibration curve was used to convert the emf readings of

the bone ash solutions to fluoride concentration. The results on replicate

analyses of a single sample solution were highly reproducible and agreed

well with the results obtained by a reference method. The authors believe

that similar procedures would be applicable to the determination of

fluoride in the ash of other normal and pathological calcifications, e.g., kidney stones. In the area of fluoride air pollution by industry, the presence of certain

fluoride compounds (such as HF, SiF4, and H^SiFe) in excess can cause

harmful effects on vegetation. The absorption of fluoride into the leaf is cumulative and will result in necrosis of the leaf Vegetation which has

been seriously contaminated in this way by air pollution can subsequently cause fluorosis when ingested by animals.

A procedure for the determination of water-soluble fluoride in air and

stack gas at ambient levels of 1 /itg/m^ or less has been described [21] in
ANALYTICAL TECHNIQUES AND APPLICATIONS 393

which the gaseous and particulate fluoride are quantitatively collected by

filtration and chemisorption on cellulose acetate filters impregnated with

sodium formate. Aluminum and iron, present in most atmospheric samples, are prevented from interfering by complexation with an added sodi- um citrate buffer, which also maintains a pH of 7.5 and controls the total ionic strength of the solution. Comparison of this technique with the

Spadns-zirconium lake method for the analysis of stack gas samples has

shown these methods to be statistically equivalent. The authors conclude

that the fluoride electrode technique is more rapid, convenient, and ap- pears to be less susceptible to interferences than existing methods for determining fluoride to levels as low as 0.25 ppb.

In oceanography, the variations of fluoride concentration in sea water

may have a possible correlation to submarine volcanic activity or out- crops of fluorine-rich minerals. Previous studies using colorimetric

methods have located anomalously high fluoride/chloride ratios in several

deep water locations of the North and South Atlantic. These studies suf- fered from the basic disadvantages of sampling by hydrographic casts,

i.e., 1) the delay between sampling and analysis, and 2) the discontinu- ous nature of the sampling. Using a unique device developed by Spencer

and Brewer [22,23] for measuring continuous F /Cl" profiles, these two

problems have been overcome. In this method, a fluoride electrode is in- corporated into an in situ meter with a chloride reference electrode. The

electrode pair is mounted on a piston floating in silicone oil which pro- vides pressure equalization and electrical insulation simultaneously. The

necessary electronic components are battery operated and located in a

pressure housing adjacent to the electrodes to minimize noise pickup. The

entire unit is self-contained and is lowered on hydrographic wire. Novel

features incorporated into the design of this device include the replacement of the internal filling solution of the electrode with gelled sea water

to counteract changes in the activity of the measured medium with temperature and also to enable the measurement of emf about a null point.

The chloride ion-selective reference electrode is also filled with sea

water; thus the whole system measures the parameter of interest: the

fluoride to chlorinity ratio. Although this device operates as well as ex- pected, it appears that fluoride variations in sea water are rare (if they occur at all), since measurements made during two cruises did not detect

any variations. However, this study has shown that devices of this type

are definitely feasible and provide a convenient method for deep sea

monitoring. The use of ion-selective electrodes in conjunction with deep

submersibles is extremely attractive since these techniques are for all practical purposes the only way chemical measurements can be made

directly from these craft. The future of ion-selective electrodes in oceanographic research is promising but not without first overcoming some extremely difficult
394 ION-SELECTIVE ELECTRODES

problems. Some of the more formidable ones include the fact that the

ratios of the major ions to chlorinity are remarkably constant, and none of

the presently available electrodes have a high enough precision to be useful. Also, many of the elements which do exhibit a wide range of concentrations, such as the transition metals, are present only at the parts per bil- lion level, and the development of electrodes to detect such species looks

doubtful at the present time. The most fruitful area for research would seem to be electrode studies of nutrients, such as nitrate, phosphate, and

silicate, which exhibit wide variations in sea water although they, too, are present at very low concentrations. It might be easiest to sum up the fu- ture of ion-selective electrodes in oceanographic studies by describing the

characteristics of the ideal electrode [23]. Such an electrode would be

capable of good response in the parts per billion range, tolerant of massive

excesses of Na+, Mg++, Ca^+, K+, CI", and Br", and would have a fairly

low impedance for working in this salty environment.

The microdetermination of fluorine in organic compounds is beset by

many difficulties in both the decomposition and determination

procedures. Recently, a procedure has been proposed by Light and Mannion [24] which employs a potentiomdtric titration of fluoride with thori- um and a fluoride electrode for end point detection. In contrast with Lingane's conclusion [18], these authors found that thorium gave a better

end point "break" than did lanthanum (see Fig. 6) which apparently is due

to the differences in the system backgrounds (neutral, unbuffered and

70% ethanol vs. 0.0 IM nitric acid and 80% ethanol). The unique features

of their decomposition procedui-e include the use of a clear, polycarbonate flask instead of glass for the oxygen combustion and dodecyl al- cohol as a combustion accelerator. The results of determinations on typical microchemical fluorine compounds, containing 13 to 76% fluorine, in the sample range of 1 to 10 mg

were within ± 0.3% (absolute) of the theoretical fluorine content, and the

standard deviation for 25 determinations was 0.2%. But as has been

pointed out many times and in many ways before, the analysis of fluorine

is a highly subjective art, and the proof of this technique awaits its ac- ceptance by other microchemists.

Additional fluoride references are addended to this chapter.

B. Calcium

The calcium ion-selective electrode is probably the second most important non-glass type of electrode developed to date, if total number of

publications and diversity of application are any sort of criteria. Included

in this wide variety of applications are: studies of scale formation; monitoring calcium levels in food processing; determining the calcium content

of minerals, pharmaceuticals, fertilizers, and explosives; and, in
ANALYTICAL TECHNIQUES AND APPLICATIONS 395

250

o 150

100

VOLUME , TITRANT Figure 6. Titration of fluoride with thorium and lanthanum in 0.01 M HNO3 and 80%

ethanol solutions. From T. S. Light and R. F. Mannion [24].

biomedicine,the study of calcium in teeth, bone, and serum (see Chapt. 7). For the determination of ionic calcium in serum and other biologic

fluids, a special electrode device has been developed for anaerobic,

flow-through measurements on only 200 fA of sample (Orion, Model

99-20 Serum Calcium Activity Flow-Thru System). A precision syringe

pump delivers the solution anaerobically through the calcium and

reference electrode system. The calcium electrode was developed especially for serum measurements and has a higher selectivity for calcium over sodium and potassium.

In addition to the calcium liquid ion-exchange electrode, a solid ion-exchange type has recently been developed [25] and evaluated [26]

by direct potentiometry and in potentiometric titrations. This type of elec- trode exhibits an improved calcium/hydrogen ion selectivity and is suited

to both analytical and biochemical measurements.

An early paper by King and Mukherji [27] describes the complexometric titration of calcium with di-sodium EDTA at a pfl adjusted to about

10 with NH4OH. Beyond the end point, the potential remains fairly constant or rises slightly due to the response of the electrode to sodium added

with the EDTA (see Fig. 7). Other divalent cations, which complex with

EDTA, and the fluoride, carbonate, and oxalate anions interfere with the

titration.
396 ION-SELECTIVE ELECTRODES

>

E

VOLUME, EDTA TITRANT

Figure 7. Titration of calcium with EDTA.

A Standard addition procedure for the determination of calcium in beer

offers the same precision as the standard EDTA titration at the normal

calcium levels in beer, but is considerably more convenient to perform

[28]. The method assumes that a 50 to 100-fold excess of complexing

agents, e.g., proteins, is present in the beer samples. After determination

of the electrode response slope with standard solutions, only two emf

measurements are required; one prior to and one after the addition of the

known calcium increment to the beer sample. A simple equation is then

used to calculate the total calcium level in the original solution.
ANALYTICAL TECHNIQUES AND APPLICATIONS 397

Muldoon and Liska have compared an ion-exchange method with the

direct potentiometric determination of calcium in skim milk [29,30]. The

two techniques were used in a study on the effect of heat treatment on the

level of ionized calcium in skim milk. Statistical analysis of the data

showed that there was no significant difference between the results obtained by the two methods on raw, pasteurized, and sterilized milk.

Results indicated that the pasteurization process significantly lowers the

ionized calcium level while rapid sterilization has little effect. In addition

to accuracy, the electrode technique offered the advantages of con- venience and repeatability.

The calcium electrode has also been applied to sea water determinations using direct potentiometric measurements [31]. The electrode is calibrated using solutions with backgrounds so like sea water that activity

coefficients can be assumed constant, and the empirical electrode equation is written in terms of concentration rather than activity. The results obtained indicate that the ionized calcium concentration in sea water is 0.0086 ± 0.0002M, which corresponds to about 84% of the total calcium

concentration at the 1 9.373 parts per thousand chlorinity level. Dyrssen [32], in attempting to obtain a precision of at least 0.1% for calcium in sea water by the potentiometric titration of calcium with

EGTA [ethyleneglycol bis(2-aminoethylether)tetraacetic acid], found

that the sodium in sea water interfered with the titration by limiting the

emf break in the vicinity of the equivalence point. That is, as the calcium

level is reduced by the titration reaction, the electrode becomes poised by

and responsive to the high level of sodium in the system and no longer senses changes in the calcium activity.

Several other applications of the calcium electrode are listed in the ad- dendum.

C. Nitrate

The nitrate electrode should be of considerable importance in the pharmaceutical, explosive, and photographic industries, but especially in the areas of agricultural analysis and pollution control. It is used for the deter- mination of nitrate in biological materials, fertilizers, and soils. In addition, this electrode can be used for nitrite determinations in cases where

it is convenient to oxidize the nitrite to nitrate. Direct nitrite measure- ments are not recommended.

In soil and ground water, the amount of nitrate present is an indication

of fertility and possible pollution due to excessive fertilization. The pollution problem arises when the nitrate (and phosphate) from agricultural fer- tilization enters streams and lakes (reservoirs) causing excessive aquatic

plant growth and eutrophication.
398 ION-SELECTIVE ELECTRODES

The direct determination of water soluble nitrate in soil using the nitrate electrode is superior to the standard colorimetric brucine method [33]. It

is suitable for both laboratory and field analyses since determinations can

be made directly on soil slurries when it is not convenient to filter the

prepared soil samples. Determinations were reportedly made with an

error of about 5% in the 2 to 30 ppm NO.r (as nitrogen) range. Standard

deviations of 12.5% were found for laboratory determinations and about

25% for measurements made directly on soil slurries. Again, the electrode

method exhibits greater convenience over earlier techniques without

sacrificing the reliability of the results. The nitrate content of plants is critical for proper growth and maximum

yield and excessive amounts may be dangerous to infants. In the

technique developed by Paul and Carlson [34], the aqueous extract of

dried plant tissues in the 1 to 50 ppm range is determined by direct potentiometry. The nitrate-selective electrode response is linear over this range. A cation exchange resin in the aluminum form is added during extraction to eliminate interference by bicarbonate and to reduce organic

anion interferences. A resin in the silver form added during the extraction

will remove any chloride interference. For practical purposes, the elec- trode technique agreed closely enough with the usual phenoldisulfonic

acid method for it to be used in the latter's place. The average relative standard deviation for the 16 plant materials studied was 3.1% for the

electrode method.

Two other nitrate references are given in the addendum.

D. Tetrafluoroborate (Boron)

Another element of interest to the agricultural chemist and to materials

scientists working with alloys, refractory compounds, semiconductors,

paints, and heat-resistant glasses is boron. This element can be easily con- verted to the fluoroborate (tetrafluoroborate) ion by reaction with

hydrofluoric acid and then measured potentiometrically. A simple ion

exchange procedure to perform this conversion has been described by

Carlson and Paul [35]. In addition, they describe a potentiometric measurement procedure for fluoroborate concentrations down to lO W. In- terferences from several anions and the rate of formation of fluoroborate

in solution were also studied. It was found that anion interference

problems and the slow rate of fluoroborate formation in solution can be overcome by the column technique described in their paper. Boron

can be readily concentrated from dilute solutions using this procedure.

A subsequent paper by Carlson and Paul describes the potentiometric

determination of boron in agricultural samples [36]. The boron conversion

and electrode determination procedures are the same, but more details are given on materials and methods. To increase the sensitivity of the
ANALYTICAL TECHNIQUES AND APPLICATIONS 399

method, the final solution volume is decreased (from 25 ml [35] to 10 ml,

i.e., a 2.5-fold increase in sensitivity) by using 50 ml polycarbonate centrifuge tubes as the sample vessels. Results from electrode determinations on water, soil, and plant samples are compared with those determined by

a modified curcumin method. The electrode technique is very accurate and in excellent agreement with the curcumin method. For water samples

containing about 1 ppm boron, the average relative standard deviation

(Sr) was about 2%; for soil extracts containing 0.1 to 1.6 ppm boron,

Sr was 7.1 to 1.4%, respectively; and for plant tissue containing 5.9 to 1508 ppm boron, the Sr was 7.2 to 0.9%, respectively.

E. Perchlorate

The third in this series of liquid anion-exchange membrane electrodes

has not received the attention afforded the others. At present, published

applications of the perchlorate electrode seem to have been limited to a

single paper [37] in which the electrode is used as an end-point detector

for the potentiometric titration of perchlorate with tetraphenylarsonium

chloride. Although the titration of perchlorate with organometallic salts, including this one, is not original, the method is demonstrated to be simple

and rapid, and the accuracy and precision are at least as good as other

presently available methods for determining perchlorate. Based on

replicate determinations on three perchlorate samples, the overall 95%

confidence limits were 0.16%. Applications of this technique include

perchlorate assay by chemical manufacturers and in determining

perchlorate in explosives and solid propellants.

This study reports that the perchlorate electrode also responds to per- manganate, periodate, and dichromate ions. The response curves for

these ions are linear over approximately the same concentration range as perchlorate, but the selectivity ratios for these ions were not evaluated. It was suggested that this electrode might be useful as an indicator for titra- tions involving these ions. F. Halides

The halides, with the exception of fluoride, have for many years been

determined potentiometrically using silver-silver halide electrodes. With

the development of halide electrodes of the membrane type, which are more resistant to surface poisoning, need no preconditioning or anodizing

treatments, and, most importantly, can be used in the presence of oxidizing agents, new areas of application have opened up as a result of these

improved characteristics. Furthermore, the convenience of these elec- trodes has resulted in their use for the more conventional measurements

in place of the traditional halide-film electrodes.
400 ION-SELECTIVE ELECTRODES

At present there exist heterogeneous and solid-state membrane elec- trodes for chloride, bromide, and iodide, and an additional liquid

ion-exchange electrode for chloride. Techniques employing these elec- trodes are the same as have been used with the traditional halide elec- trodes, i.e., various direct potentiometric measurements and titrations,

and these require little additional comment.

The applications, however, have increased to include measurements in both aqueous and non-aqueous systems, even in the presence of oxidants. In addition, the chloride liquid ion-exchange electrode can also be used in solutions containing sulfide and reducing agents, and is less subject to in- terference from bromide and iodide than is the solid-state electrode.

The chloride electrode has been applied to chloride-level monitoring in many materials such as foods, beverages, pharmaceuticals, plastics, and

pesticides. In addition, a combination chloride electrode has been

developed for direct chloride measurements on samples as small as 10 /xl. This electrode is especially useful for rapid screening for cystic fibrosis by

measuring sweat chloride levels directly on the patient's skin and can also be used for body fluids such as saliva, urine, and cerebrospinal fluid. For

serum chloride measurements, the liquid ion-exchange electrode is more

suitable and is also available in a flow-through configuration for anaerobic

measurements.

An interesting method has been developed for the continuous monitoring of hydrogen chloride levels in gas and aerosol samples [38]. This

technique resulted from a study of the generation of volatile pyrolytic

decomposition products from a number of chlorocarbon polymers under

simulated fire conditions. The device consists of a gas scrubber to absorb

the HCl and a liquid ion-exchange chloride electrode with a flow-through

compartment to measure the chloride concentration. A syringe pump

delivers water to the top of the scrubber and withdraws sample solution

from its base at equal rates, so that the volume of water retained in the

scrubber for absorption remains constant. Over the range of 20 to 6000

ppm HCl, the reproducibility was within ± 5% for a gas sampling rate of

100 cmVmin. The response time for the system was about 1.5 min (to

reach 99% of equilibrium).

The bromide-selective electrode is of use in photographic processing,

the manufacture of pharmaceuticals, and in biomedical research. A titra- tion technique adapted from the ASTM method D1562 for the determination of epoxy equivalents by titration with HBr has been suggested in which a potentiometric end point is used in place of the crystal violet visual end point [39]. The potentiometric titration of epoxy groups is easier to automate and can be used in the presence of colored epoxies.

The iodide electrode has been used for the determination of chloride,

bromide, and iodide by a successive potentiometric titration with silver
ANALYTICAL TECHNIQUES AND APPLICATIONS 401

[40]. The error caused by the adsorption of titrant on the silver halide

precipitate was eliminated by taking the Fajans adsorption rule into ac- count and adding barium nitrate to the sample solution. The silver halides

are precipitated in the order: iodide, bromide, chloride; the end point of

each titration being indicated by a distinct potential "break" (see Fig. 8). Thus, using the procedure described, the three halides can be successively determined by a single titration carried out in a couple of minutes.

E

2 3 VOLUME , Aq* TITRANT Figure 8. Titration curve for the successive titration of chloride, bromide, and iodide with

silver, a) End point 1: I" + Ag+ = Agl(s); b) End point 2: Br" + Ag+ = AgBr(s); c) End

point 3: Ch + Ag+ = AgCl(s). From B. Csakvari and K. Meszaros [40]. A study reported by Arino and Kramer [41] may be of some interest to nuclear and radiochemists. The specific activity of was calculated

from the measured ^^^I activity and the total iodide content, the latter being determined with a heterogeneous membrane iodide electrode. It was found that radiation levels as high as twenty curies of ^^^I did not af- fect the electrode measurements. The direct potentiometric measurement

of total iodide concentration could be made in less than five minutes with

a precision of 1% (relative standard deviation).

Some additional halide references are given in the addendum.

G. Cyanide

The cyanide electrode, which presumably is a silver iodide membrane

electrode, is recommended for use in the concentration range from 10"^
402 ION-SELECTIVE ELECTRODES

to IQ-^M cyanide, although it gives a useable response from 10"^ to lO-^M cyanide. At concentrations above lO^^M, the electrode life is shortened due to the formation of soluble silver cyanide complexes result- ing in a slow dissolution of the electrode membrane. The only serious

anion interferences are sulfide and iodide, and for maximum sensitivity

the pH should be kept above 10 to prevent the lowering of the free cya- nide level by the formation of HCN.

A general paper by Pungor and Toth [42] describes a systematic study

of various metal ion complexes with cyanide using their silver iodide

heterogeneous membrane electrode. In addition to this type of study, the

cyanide electrode should be useful for industrial pollution monitoring,

measurements of free cyanide in plating bath solutions, and the deter- mination of cyanide in foods and beverages.

The above example points up an important consideration in using

ion-selective electrodes. That is, many of these electrodes can be used for the measurement of ions for which they are not nominally selective. In

other words, when the "selective ion" is absent or present in sufficiently

low concentration, it may be possible to use these electrodes for species

normally considered interferences. Such applications are another reason

for accurately evaluating and reporting the selectivity ratios for ions inter- fering with the various ion-selective electrodes. Of course, the main

reason is still that these ratios allow one to anticipate difficulties due to solution interferences which can cause erroneous results and to compensate for or eliminate these problems.

H. Silver Sulfide

The silver sulfide solid-state membrane electrode responds to both free

silver and free sulfide ions in solution. As in the case of the silver halide

electrodes, the membrane is an ionic conductor for silver ions, and the

emf developed corresponds to the ionic distribution of silver ions between

the sample and inner reference solution. This distribution in turn depends on the activity of the silver ions in the sample solution, since the

inner reference solution is of constant silver acfivity. The electrode also responds to sulfide ion since the silver acfivity is dependent upon the sul- fide activity as related through the silver sulfide solubility product.

The electrode will respond to concentrations between 1 and IQ-'^M in total silver or sulfide, or to free sulfide ion acfivifies down to lO-^'M or below in the presence of sulfide complexes, and to free silver activities to

10-25yv/ in the presence of complexed silver ion. In fact, studies in this laboratory [43] indicate that the response to free silver ion is Nernsfian

from 10"W down to IQ-^^M on sample volumes of 5 /jlI. This is equivalent to a probability of much less than one ion of free silver in this volume of test solution and indicates that the electrode at some point
403

begins to respond to the complexed silver. The results of this study

are shown in Figure 9 where the solid line is the theoretical Nernst

slope, and the dashed line indicates the electrode response to total silver ion activity in silver nitrate solutions.

24 22 20 18 16 14 12 10 8 6 4 2 pAg

Figure 9. Silver sulfide electrode response to silver activity (test solution vol. = 5yLtl)

(Solid line: 59.2 mV/pAg) ~ pAg

Point Solution Composition (calc) E(mV)

1 lO-'M AgNOs 1.1 + 550

2 10-W AgNOa 3 + 438

3 10-W AgNOa 4 + 385

4 10-W AgNOs 5 + 323

5 lO W AgNO.5 6 + 260

6 lO W AgNO.i 7 + 225

7 10-W AgNO:, 8 + 213

8 sat'd Agl 8.2 + 150

9 sat'd Agl+ 10-«M KI 10.3 + 21 10 sat'd Agl + 10-W Kl 12.3 -91

1 I sat'd AgCl + lM Na.S-.O., 14.2 -256

12 sat'd AgCl + O.lM Kl 15.5 -298

13 O.IM Na2S+ \M NaOH 24.9 -872
404 ION-SELECTIVE ELECTRODES

The use of this electrode for the direct potentiometric determination of

silver at the parts per billion level is presented in a paper by Muller, et al. [44] in which the response of the electrode is found to be linear and

Nernstian down to 13.5 ppb(1.2 x 10-"M Ag*).

In addition to trace and microchemical determinations, the silver sul- fide electrode can be widely applied. As a sulfide electrode, it serves as a

pollution monitor for industrial waste both in water supplies directly and

in the air by aqueous absorption of the gaseous sulfides. Sulfide levels in

drilling muds are of interest to petroleum chemists and, in the paper industry, the sulfide concentration in pulping liquors can be measured.

For silver determinations, the only interference is mercuric ion, which

forms the highly insoluble mercuric sulfide (approximately the same order

of solubility as Ag2S). In basic solutions, silver ion will precipitate as Ag20 unless prevented by the presence of high enough levels of silver
ANALYTICAL TECHNIQUES AND APPLICATIONS 405

complexing agents, in which case only the free silver ion is detected unless a standard addition technique is used. As a sulfide detector, the elec- trode is interference-free, but again pH will affect the amount of free sul- fide ion in solution. In all but the most basic solutions, sulfide will complex with hydrogen ion to form HS" or H2S. In such cases, total sulfide can be found by calculation using hydrogen sulfide equilibrium data, by

titration with silver, or by a standard addition procedure.

600

4 00

200

eq.pt. VOLUME , TITRANT

Figure 1 \. Titration of silver with sulfide. End point occurs at 98% of theoretical equiv- alence point. From T.-M. Hseu and G. A. Rechnitz [46J. As in the case of the silver halide electrodes, the absence of the metallic

silver phase in the electrode membrane permits the use of this electrode

in solutions containing oxidizing agents. An example of this type of inter- ference is shown in Figure 10 where the silver sulfide membrane and

silver-silver sulfide electrodes are used in AgNO,} titrations of chloride

solutions containing a large quantity of ferric ion and \M in nitric acid

[45]. In this titration, the silver sulfide membrane electrode is unaffected

by the strong oxidants and indicates a typical titration curve and the cor-
406 ION-SELECTIVE ELECTRODES

rect end point. However, the silver-silver sulfide electrode shows a

smaller end-point break which occurs well in advance of the true equivalence point. In another analytical study of the silver sulfide electrode [46] , the sensitivity, selectivity, and response characteristics are evaluated. In the

titration of silver nitrate with standard sodium sulfide, it is shown (see

Figure 1 1) that the inflection point of the titration occurs at 98% of the

theoretical equivalence point due to the hydroxide ion (formed by hydrolysis of the sulfide) present in the titrant. That is, the hydroxide ion con- sumes silver by the formation and precipitation of silver hydroxide, i.e., hydrated silver oxide. However, by standardizing the sodium sulfide

titrant by potentiometrically titrating a standard silver nitrate solution, the

effect of sulfide hydrolysis can be compensated by inclusion in the titre of

the sulfide titrant. In this way, the inflection point of the titration curve

will correspond to the equivalence point.

Additional references to applications of the silver sulfide electrode are given in the addendum.

I. Divalent Cations (Magnesium)

The divalent cation electrode, developed primarily for water hardness

measurements, exhibits an approximately equal selectivity for all divalent

cations and only a limited response to sodium, potassium, and hydrogen

ions. Although only one paper has been pubHshed in this area [47], the

determination of water hardness is important in studies of scale formation, efficiency of water softeners, and as monitors of hardness in untreated waters. It is assumed, therefore, that this type of electrode has

been used much more than is indicated by published studies. Another application of this electrode is in the determination of specific

divalent cafions when others do not present a serious interference. An ex- ample of this is given by the direct potentiometric measurement of magnesium in sea water [48]. In this case, the electrode is calibrated with

solutions already containing the various competing ions and varying only

in the concentration of the magnesium ion. An ionized magnesium concentration of 0.048M was found for I. A. P.O. (International Association

of Physical Oceanography) sea water (chlorinity 19.373 ppt) of 0.0534M

total magnesium content. From this, it is concluded that about 90% of the sea water magnesium is ionized. Using an activity coefficient of 0.36, the

activity of magnesium in sea water is calculated to be 0.0173M.

This application represents another case where one of the ion-selective

electrodes is used to determine an ion for which it is not specifically

named (the manufacturer does suggest its use in determining calcium

and magnesium), although it is not as extreme a situation as using an

iodide electrode for the determination of cyanide, which under normal
ANALYTICAL TECHNIQUES AND APPLICATIONS 407

circumstances is an interference in the measurement of iodide. It is significant, however, that the divalent cation electrode is responsive

to any and all of the divalent ions, in the order: Pb++ > Zn++ = Fe++

> Cu++ > Ni++ > Ca++ = Mg++ > Ba++ > Sr++. In addition to the direct

potentiometric measurement of these ions, the electrode can be used as the end-point detector in the titration of these ions with EDTA or other

chelators.

J. Copper (Cupric Ion)

Although the original cupric ion-selective electrode was a liquid

ion-exchange type, a solid-state membrane electrode has been recently

developed which exhibits greatly improved characteristics. The liquid

ion-exchange electrode was useful, as evidenced by its application

to the study of the formation of copper complexes [49], but was Hmited

to copper concentrations above about 10~W and was plagued by a large

number of interferences, both cationic and anionic. On the other hand, the

solid-state electrode is useable down to total cupric ion concentrations of

10"W (1 ppb) and is virtually interference-free with respect to the usual

divalent cations. Electrode malfunction occurs with silver and mercuric

ions, and ferric ion must be held below one tenth of the cupric ion concentration. The latter is easily accomplished by adjusting the sample pH to above 4. The potential applications of a cupric ion electrode are many-fold and

range from the measurement and control of copper levels in plating baths

and etching baths for printed circuits to determining copper in various

materials such as pharmaceuticals, foods, algaecides, and pesticides. With

the importance of copper in today's commerce, it is likely that this elec- trode will prove to be a valuable analytical tool. K. Lead AND Cadmium

As in the case of the cupric ion electrode, the original liquid

ion-exchange electrode for lead ion has been supplanted by a solid-state membrane electrode. This has again resulted in an extension of the useable range from 1 0' Wlead for the liquid ion-exchange electrode to 1 0-

W

for the new electrode. The number of interferences has similarly been

reduced to silver, mercury, and copper which must be absent from the test solution and cadmium and ferric ion, which should not exceed the lead ion

concentration.

Lead ion can be determined by direct potentiometry and by titrations with EDTA or oxalate. The applications of this electrode include water

and air pollution studies and the measurements of lead levels in food

products, biological fluids, and various manufactured materials such as

paints, glass, and pesticides.
408 ION-SELECTIVE ELECTRODES

The cadmium solid-state electrode has similar response characteristics,

i.e., total cadmium measurements down to lO'W and interference by

silver, mercury, copper, ferric ion, and lead. L. Sulfate and Phosphate

Analytical studies with prototype heterogeneous membrane electrodes

sensitive to SOi~ and PO^^" were found useful for direct potentiometry

and potentiometric titrations under very limited circumstances [50] . The

sulfate electrode gave a useful response to concentrations as low as lO-'W SO3" and was approximately Nernstian above lO'^M. The

potential of the phosphate electrode was less stable, drifting as much as

1 mV over a 10-min period. A crude calibration curve for phosphate was

constructed over two decades of concentration, 10-^ to 10~W, with a

slope of only 7 mV/pP04 (theoretical: ~ 20 mV/pP04).

Since neither electrode was particularly selective for its primary ion,

they are probably best used as end-point detectors in potentiometric titra- tions where selectivity is not of utmost concern. Due to their unsatisfactory behavior for general solution measurements, these electrodes are not now commercially available, but it is hoped that improved versions will become available for the determination of these very important ions. For the present, one possible procedure for the potentiometric deter- mination of sulfate involves the titration of sulfate with standard lead

perchlorate using a lead electrode as the end-point detector [51]. The

lead sulfate precipitation is complete enough to provide a very good

potential break at the end point of the titration (total emf change approximately 200 mV for the titration of millimolar sulfate in 50% dioxane

solution). Although direct and continuous monitoring of sulfate is still not feasible, except perhaps by a continuous process titrator (Chapt. 10),

the lead electrode titration procedure can be used to detect harmful

sulfate levels in water supplies and to check the effectiveness of sulfate removal processes. M. Thiocyanate

The solid-state thiocyanate electrode responds to thiocyanate concentrations as low as lO'W but cannot be used in reducing solutions or solu- tions containing species that form silver complexes or insoluble silver

salts. N. Miscellaneous

A recent paper by Coetzee and Preiser [52] describes the development

of liquid-liquid membrane electrodes which respond to various organic

and inorganic anions. Based on one of many possible solvent extraction
ANALYTICAL TECHNIQUES AND APPLICATIONS 409

systems, these electrodes use the salts of the methyl tricaprylyl ammonium cation dissolved in 1-decanol as the organic phase components. The

electrodes exhibit a useful concentration range of IQ-^ to IQ-^ or IQ-^M

for perchlorate, chloride, bromide, iodide, nitrate, sulfate, thiocyanate.

Na Rb Cs Figure 1 2. Response of nonaction homolog membranes to monovalent cations. (AE/decade

change in cation concentration.) From Z. Stefanac and W. Simon [53]. p-toluenesulfonate, acetate, formate, propionate, oxalate, and benzoate,

and 10-1 iQ lO-^M for salicylate. Most of the electrodes give an essentially Nernstian response which is linear over about two decades of concentration from approximately 10"^ to IQ-^M.

Ion-association extraction systems, such as described above, and

chelating extraction systems may be the forerunners of new types of

ion-selective electrodes tailored to various organic ions. Developments

along these lines could open up whole new areas for the application of

these electrodes.

Even more exotic systems in which electrochemical cells using

macrotetrolides (nonactin homologs) on various inert supports as membranes have been described [53] (see Chapt. 1 for details). These elec- trodes have a far superior selectivity for potassium over sodium than do
410 ION-SELECTIVE ELECTRODES

the presently available ion-selective glass electrodes. In Figure 12. the

response of nonactin homolog membranes is given in terms of the emf

change produced when the cation concentration is increased by one order

of magnitude. Over the concentration range of 10-^ to 10~W potassium

chloride the response slope was approximately 32 mV/pK. By modifying

the inert supports, the authors believe the speed of response (~ 2 hours

for equilibrium) may be increased by orders of magnitude, and the

response slope may become Nernstian.

O. Conclusion

In the discussions above, a brief survey of a very extensive topic was

attempted. Many of the common applications and procedures were

omitted in favor of presenting some of the more recent studies using

ion-selective electrodes as they have appeared in publications over the

past several years. Unfortunately, the newness of many of these elec- trodes has necessitated the very cursory treatment, especially concerning

applications, given to several of the electrodes. Although some of the

material dealing with electrode characteristics had been presented in earlier chapters, it was felt that some repetition was necessary to discuss

the analytical uses and limitations of these electrodes properly.

The prospects for the future of ion-selective electrodes for analytical

applications would seem to be bright indeed. This outlook not only in- cludes the development of new electrodes, selective for many different

ions and perhaps based on new systems for achieving better specificity,

but also continuous and even automated analyses in which computers

digest the data received directly from banks of miniaturized ion-selective

electrodes and, using information on selectivities, simultaneously evaluate and print out the concentrations of dozens of ions in solution. Indeed,

in such rapidly growing areas as oceanography, pollution, and

biomedicine where rapid, or on-site, and often continuous monitoring and

analysis are needed, the convenience of ion-selective electrode systems

offers many advantages over more conventional techniques. In other

areas of analysis, ion-selective electrodes will doubtless supplant many of

the more ''sophisticated" methods simply on the basis of their many su- perior characteristics. At present, research scientists working with these sensors are at the forefront of a new and rapidly developing technology—a renaissance of analytical potentiometry. V. Addendum

Supplementary References A. General Applications

"Membrane Electrodes in Chemical Analysis", Pungor. E..Toth. K..and Havas.J.. Hung.

Sci. Instr. 3, 2 (1965).
ANALYTICAL TECHNIQUES AND APPLICATIONS 411

"Membrane Electrodes Respond to Anions", (anonymous), Chem. Eng. News, Jan. 31, 1966, p. 24. "Ion-Selective Electrodes", Rechnitz, G. A., Chem. Eng. News, June 12, 1967, p. 146. "Selective Ion Electrodes", Light, T. S., Analysis Instrumentation 1967, L. Fowler, a/., Eds., Plenum Press, New York, 1967. "Study on Ion Selective Electrodes", Pungor, E., Hung. Sci. Instr. 10, 1 (1967). "Theory and Application of Anion Selective Membrane Electrodes", Pungor, E., Anal. Chem. 39, 28A (1967). B. Fluoride

"Electrode for Sensing Fluoride Ion Activity in Solution", Frant, M. S., and Ross, J. W.,

Jr., Science 154, 1553 (1966). "Fluoride in Chromium Plating Baths: Determination of Activity and Concentration",

Frant, M. S., Plating 54, 702 (1967). "Direct Determination of Fluoride in Tungsten Using the Fluoride Ion Activity Electrode", Raby, B. A., and Sunderland, W. E., Anal. Chem. 39, 1304 (1967). "Modification of the Fluoride Activity Electrode for Microchemical Analysis", Durst,

R. A., and Taylor, J. K., Anal. Chem. 39, 1483 (1967). "Potentiometric Titration of Fluoride with Tetraphenylantimony Sulfate", Orenberg, J. B., and Morris, M. D., Anal. Chem. 39, 1776 (1967). "The Rapid Determination of Fluoride in Mineral Fluorides Using a Specific Ion

Electrode", VanLoon, J. C, Anal. Lett. 1, 393 (1968). "Lanthanum Fluoride Electrode Response in Aqueous Chloride Media", Mesmer, R. E., Anal. Chem. 40, 443 (1968). "Activity Measurements with a Fluoride-Selective Membrane Electrode", Srinivasan, K., and Rechnitz, G. A., Anal. Chem. 40, 509 (1968). "Evidence that there are Two Forms of Fluoride in Human Serum", Taves, D. R., Nature

217, 1050 (1968). "Determination of Fluoride in Mineralized Tissues Using the Fluoride Ion Electrode", McCann, H. G., Archs. Oral Biol. 13, 475 (1968). "Clearance of Fluoride from the Mouth after Topical Treatment or the Use of a Fluoride Mouthrinse", Aasenden, R., Brudewold, F., and Richardson, B., Archs. Oral Biol. 13, 625 (1968). "Determination of Fluorine in Feeds by the Fluoride Ion Activity Electrode", Torma, L., and Ginther, B. E., J. Assoc. Offic. Anal. Chem. 51, 1177 (1968). "An Evaluation of Some Methods for the Determination of Fluoride in Potable Waters and

Other Aqueous Solutions", Crosby, N. T., Dennis, A. L., and Stevens, J. G., Analyst 93, 643 (1968). "Determination of Submicromolar Concentrations of Fluoride in Biological Samples",

Taves, D. R., Talanta 15, 1015 (1968). "Evaluation of the Lanthanum Fluoride Membrane Electrode Response In Acidic

Solutions: The Determination of the pK„ of Hydrofluoric Acid", Vanderborgh, N. E., Talanta 15, 1009 (1968). "Lanthanum Fluoride Electrode Response in Water and in Sodium Chloride", Warner,

T. B., Anal. Chem. 41, 527 (1969). C. Calcium

"Calcium-Selective Electrode with Liquid Ion Exchanger", Ross, J. W., Science 156, 1378 (1967).
412 ION-SELECTIVE ELECTRODES

"Calcium Electrode Method for Measuring Dissociation and Solubility of Calcium Sulfate Dihydrate", Nakayama, F. S., and Rasnick, B. A., Anal. Chem. 39, 1022 (1967). "Ion Specific Membranes as Electrodes in Determination of Activity of Calcium",

Shatkay, A., Anal. Chem. 39, 1056 (1967). "Calcium and the Control of Mitosis in the Mammal", Perris, A. D., and Whitfield, J. F., Nature 216, 1350 (1967). "Cation Measurements in Biological Materials", Moore, E. W., Ann. N. Y. Acad. Sci. 148, 93 (1968). "Determination of Calcium and Oxalate with an Ion-Exchange Electrode", Mukherji, A. K., Anal. Chim. Acta 40, 354 (1968). "Electrode Determination of Salivary Calcium Ion Activity", Gron, P., Spinelli, M. A., and Hay, D. I., lADR Abstracts, p. 58 (1968). "Measurement of Serum Ionic Calcium Using a Specific Ion Electrode", Arnold, D. E., Stansell, M. J., and Malvin, H. H., Amer. J. Clin. Path. 49, 627 (1968). "Use of Calcium-Selective Electrode to Measure Ionized Calcium Levels in Normal and

Pathological Plasma", Oreskes, I., and Douglas, K. S., Clin. Chim. Acta 21, 303 (1968). "Studies with Ion-Exchange Calcium Electrodes: The Distribution of Ionized Calcium

between Blood and Cerebrospinal Fluid in Man and Dog", Moore, E. W., and Blum, A. L.,

J. Clin. Invest. 47, 70a (1968). "Potentiometric Measurements with Calcium-Selective Liquid-Liquid Membrane

Electrodes", Rechnitz, G. A., and Lin, Z. F., Anal. Chem. 40, 696 (1968). "Comparison of a Liquid Ion Exchange Electrode and the AOAC Method for Determining

Calcium in Animal Feeding Stuffs", Allen, R. D., Hobley, J., and Carriere, R., J. Assoc.

Offic. Anal. Chem. 51, 1181 (1968).

D. Nitrate

"An Evaluafion of the Performance of the Nitrate-Selective Electrode", Potterton, S. S., and Shults, W. D., Anal. Lett. 1, 1 1 (1967). "Use of a Selective Ion Electrode for Determination of Nitrates in Soils", Bremner, J. M., Buddy, L. G., and Agarwal, A. S., Anal. Lett, (in press).

E. Halides

"Analytical Study of an Iodide-Sensitive Membrane Electrode", Rechnitz, G. A., Kresz, M. R., and Zamochnick, S. B., Anal. Chem. 38, 973 (1966). "Study of Iodine Complexes by Means of the Membrane Electrode, System Pungor",

Burger, K., and Pinter, B., Hung. Sci. Instr. 8, 11 (1966). "Potentiometric Measurements with Chloride-Sensitive and Bromide-Sensitive Membrane

Electrodes", Rechnitz, G. A., and Kresz, M. R., Anal. Chem. 38, 1786 (1966). "Analytical Applications of Bromide and Chloride Ion-Selective Membrane Electrodes", Havas, J., Papp, E., and Pungor, E., Magy. Kem. Foly. 73, 292 (1967). "Analytical Application of Iodide-Selective Rubber Membrane Electrode, I.", Havas, J., Huber, M., Szabo, I., and Pungor, E., Hung. Sci. Instr. 9, 19 (1967). "Sweat Chloride Analysis by Chloride Ion-Specific Electrode Method Using Heat

Stimulation", Hansen, L., Buechele, M., Koroschec, J., and Warwick, W. J., Amer. J. Clin. Path. 49, 834 (1968). "Dead Sea Brines: Degree of Halite Saturation by Electrode Measurement", Lerman, A., and Shatkay, A., Earth Plan. Sci. Lett. 63, 5 (1968).
ANALYTICAL TECHNIQUES AND APPLICATIONS 413

F. Silver Sulfide

"Specific Ion Determination of Hydrogen Sulfide in Beer", Owades, J. L., Blick, R., and Owades, S. H., A.S.B.C. Proc, 1967. "Bestimmung von Sulfid mit einer Sulfidionen-empfindlichen Elektrode", Bock, R., and

Puff, H. J., Z. Anal. Chem. 240, 381 (1968). VI. References

deBrouckere, L., Bull. Soc. Chim. Belg. 37, 1 03 ( 1 928). Malmstadt, H. V.. and Winefordner, J. D., Anal. Chim. Acta 20, 283 (1959). Malmstadt, H. V.. and Pardue, H. L., Anal. Chem. 32, 1034 (1960). Malmstadt, H. V., Hadjiioannou, T. P., and Pardue, H. L., Anal. Chem. 32, 1039

(1960). Malmstadt, H. v., and Winefordner, J. D.. Anal. Chim. Acta 24, 91 (1961). Durst, R. A., Anal. Chem. 40, 93 1 ( 1 968). Durst, R. A., and Taylor, J. K., Anal. Chem. 39, 1374(1967).

Durst, R. A., May, E. L., and Taylor, J. K., Anal. Chem. 40, 977 ( 1 968). Frant, M. S., and Ross, J. W., Anal. Chem. 40, 1 169 (1968). Baumann, E. W., Anal. Chim. Acta 42, 127(1 968). Ross, J. W., Jr., paper presented at the Amer. Microchem. Soc. Workshop, Penn.

State Univ., Aug. 1968. Durst, R. A., Mikrochim. Acta 3, 611 (1969). Durst, R. A., and Ross, J. W., Jr., Anal. Chem. 40, 1343 (1968). Gran, G., Acta Chem. Scand. 4, 559 (1950); see also Anfalt, T., Dyrssen, D., and

Jagner, D., Anal. Chim. Acta 43, 487 (1968). Baumann, E. W., Anal. Chem. 40, 1731 (1968). Bock, R., and Strecker, S., Z. Anal. Chem. 235, 322(1 968). Lingane, J. J., Anal. Chem. 39, 88 1 ( 1 967). Lingane, J. J., ibid. 40, 935(1 968). Shane, N., and Miele, D., J. Pharm. Sci. 57, 1 260 ( 1 968).

Singer, L., and Armstrong, W. D., Anal. Chem. 40, 6 1 3 ( 1 968).

Elfers, L. A., and Decker, C. E., Anal. Chem. 40, 1 658 ( 1 968). Spencer, D. W., Woods Hole Oceanographic Inst., private communication,

Sept. 1967. Brewer. P. G., Woods Hole Oceanographic Inst., private communication, Dec.

1968.

Light, T. S., and Mannion, R. F., Anal. Chem. 41 , 1 07 ( 1 969). Schultz, F. A., Petersen, A. J., Mask, C. A., and Buck, R. P., Science 162, 267

(1968). Rechnitz,G. A., and Hseu,T. M., Anal. Chem. 41, 1 1 1 (1969). King, J. A., and Mukherji, A. K., Naturwissenschaften 24, 702 (1966). Orion Applications Bulletin No. 8, "Determination of Total Calcium Levels in Beer

Using the Calcium Ion Activity Electrode", Orion Research, Inc. (1968). Liska, B. J., Purdue Univ., private communication, 1968. Muldoon, P. J., and Liska, B. J., J. Dairy Sci. 52, 460 ( 1 969). Thompson, M. E.,and Ross, J. W.,Jr., Science 154, 1643 (1966). Dyrssen, D., Univ. of Gothenburg (Sweden), private communication, 1968. Orion Applications Bulletin No. 6, "Determination of Nitrate in Soils with the Nitrate Ion Activity Electrode". Orion Research. Inc. ( 1968). Paul, J. L., and Carlson. R. M.,J. Agr. Food Chem. 16,766(1968).

Carlson, R. M.,and Paul, J. L.,Anal. Chem. 40, 1292 (1968).
414 ION-SELECTIVE ELECTRODES

[36] Carlson, R. M., and Paul, J. L., Soil Sci. (in press). [37] Baczuk, R. J., and DuBois, R. J., Anal. Chem. 40, 685 ( 1 968). [38] LecT.G., Anal. Chem. 41. 391 (1969). [39] Orion Research, Inc., General Catalog, p. 5 (1968). [40] Csakvari. B., and Meszaros, K.. Hung. Sci. Instr. 11. 9 (1968).

[41 ] Arino. H.. and Kramer, H. H., Nucl. Applic. 4, 356 ( 1 968). [42] Pungor, E., and Toth, K., Hung. Sci. Instr. 14, 1 5 ( 1 968). [43] Durst, R. A., NBS, unpublished results. [44] Muller, D. C, West, P. W., and Muller. R. H.. Anal. Chem. (in press). [45] Light, T. S., and Swartz, J. L., paper presented at the Pitts. Conf. on Anal. Chem.

and Appl. Spect., Cleveland, Ohio, March 1 968.

[46] Hseu,T.-M.,and Rechnitz,G. A., Anal. Chem. 40, 1054(1968).

[47] Cummins, R. W., Deterg. Age, March 1968, p. 22. [48] Thompson, M. E., Science 153, 867 ( 1 966). [49] Rechnitz,G. A., and Lin,Z. F., Anal. Lett. 1,23 (1967). [50] Rechnitz,G. A., Lin,Z. F., and Zamochnick. S. B., Anal. Lett. 1.29(1967).

[51] Ross, J. W., Jr., and Frant, M. S., Anal. Chem. 41, 967 (1969). [52] Coetzee, C. J., and Freiser, H., Anal. Chem. 40, 207 1 (1968). [53] StefanacZ., and Simon, W., Microchem. J. 12, 125 (1967).
CHAPTER 12

SYMPOSIUM DISCUSSION

The transcription of selected segments of the discussion sessions is in- cluded in this volume because it supplements much of the material in the

preceding chapters. In this chapter will be found comments on practical

problems such as noise, interferences, and methodology and additional in- formation on the principles of operation, construction, and applications of

ion-selective electrodes.

The Symposium was arranged so as to provide time for questions at the

completion of each lecture and, in addition, a panel discussion period was

scheduled at the conclusion of each day's session at which all of the

speakers were available to answer questions and comments from the au- dience.

The following discussions were transcribed with a minimum of editing

and represent the spontaneous exchange of remarks of the various participants as they were recorded at the Symposium. Wherever possible, the

participants have been identified and have had an opportunity to correct

this transcription for technical accuracy.

THURSDAY MORNING SESSION

L. M. Chambers (Procter and Gamble Company}: It seems to me that one of the limitations of the liquid ion exchange membrane electrodes is going to be their use in high ionic strength media looking for low-level

materials; for example, measuring water hardness at the ppm

calcium-magnesium level where the ionic strength of your samples may

vary depending upon their source, anywhere from tenth molar on down.

We know from calibration curves that the ionic strength does have an ef- fect in a non-specific manner and, depending on the ion controlling the

ionic strength, it could also interfere such as in the case of sodium ion. I am interested in knowing if anyone has had experience in either removing

the interfering ions or using some better measurement technique.

J. W. Ross (Orion Research) : It is certainly true, as has been just mentioned, that liquid electrodes are not highly selective systems as compared

with the solid membrane electrodes, and that one does have a problem in measuring very dilute solutions of an ion in the presence of a high

ionic strength background. In the case of solid electrodes, it is possible

to get around this difficulty by intentionally adding a component to bring

the ionic strength up to a very high level and swamp out ionic strength ef- fects. If one tries this with liquid electrodes, in most situations one finds

that he is inevitably adding an interfering ion by this ionic strength buffer- 415
416 ION-SELECTIVE ELECTRODES

ing procedure. There are still ways of compensating for this, however.

One way of doing this is to measure the conductivity of the sample. You

will find that you can get a very close approximation of the ionic strength

of the sample. I would suggest that in water quality control applications

this method makes a lot of sense, since conductivity is normally one of the

parameters being measured as well as water hardness and a suitable

nomograph can be derived for computing correction factors. Slightly re- lated to this. Dr. Durst reported that EDTA-calcium titrations, using a calcium electrode, cannot be done in the presence of high sodium

backgrounds such as found in sea water; the end-point break being too

small, and this is certainly true. I would suggest here that either the

copper electrode or the cadmium electrode, as I mentioned earlier, can be

used for calcium end-point determinations by the indicator method of

Reilley. Under these circumstances, one can titrate at the ppm level of

calcium in the presence of a million-fold excess of sodium or chloride ions. Anonymous: There seems to be some question whether chloride ion in- terferes with the fluoride electrode. Would you care to comment on that?

J. W. Ross (Orion): We have observed no case of interference. The in- terference could not be serious, and you would have to work at very high

levels of chloride to be significant. One must be very careful in making up

the chloride solutions to avoid contamination by trace fluoride. Some

recent work at Oak Ridge National Laboratory has shown that apparent

chloride interferences have been due to traces of fluoride in the chloride

reagents used to make up the solutions. Again, we have not observed any

chloride interference with the fluoride electrode. R. G. Bates ( NBS): I wonder if it isn't an over-simplification to attribute

all of the departure from the Nernst equation to the activity corrections.

We have found that variation in the liquid junction potential accounts for

about one-third of the deviation. Would you agree?

J. W. Ross (Orion): I certainly would. In my discussion, I have conveniently ignored the existence of the liquid junction potential, and I am

sure that anyone familiar with pH measurements knows the problems as- sociated with this.

J. N. Butler (Tyco Laboratories): I would like to point out that the in- flection point of a titration does not necessarily coincide exactly with the

equivalence point. This must be determined either experimentally by

titration of a solution of known concentration or else by a theoretical cal- culation of all the equilibria and kinetics of the reaction. A plot of AV/AE

is not easy to interpolate in the region of the end point. One of the better

methods of determining the end point, where you do not have a dead stop

potential to work from is to calculate the concentration of the titrant ion

in the solution past the end point and extrapolate back on a linear graph of

concentration vs. volume added. This is the original Gran method and has
SYMPOSIUM DISCUSSION 417

been used successfully in a number of laboratories where people have had

to determine concentrations very accurately in solutions where there may

be impurities. Impurities show up on this plot quite clearly as deviations

from linearity. If you have very pure solutions and a very clean reaction,

you get a precisely linear plot down to something on the order of 1 0-^ or

10-6 molar. It is not as good as a dead stop potential technique to a few

millivolts, but this latter method cannot always be used.

THURSDAY AFTERNOON SESSION

J. W. Ross (Orion): There was an obvious discrepancy between the

solubility product for lanthanum fluoride determined by the electrode

solubility measurement as compared with the solubility product deter- mined from freshly precipitated lanthanum fluoride. This really shouldn't

be too much of a surprise. A single crystal will always have a solubility

product considerably smaller than the finely divided material, and this is particularly true for substances which form hard crystals, that is, where

the surface free energy of the crystal is quite large. Lanthanum fluoride is perhaps an exceptional case, but there are other examples. We have

looked at calcium fluoride which is much more soluble and easier to handle experimentally. We have measured the solubility of cleavage pieces of

single-crystal calcium fluoride against freshly precipitated calcium

fluoride and find differences of factors of a hundred between the two

methods of preparation. I found this difficult to believe when it was first pointed out to me, but it generally seems to be true. Now, as you go to softer materials such as silver chloride, where the surface free energy is much smaller, this effect is not nearly as evident. This should have been

obvious to me, being trained as an analytical chemist. That is, going back

to the idea that if I precipitate barium sulfate I can digest this precipitate

and, over a period of time, the little crystals grow bigger. This means, of

course, that the smaller crystals are more soluble than the big ones.

J. N. Butler (Tyco): I am amazed that this effect can be as large as a fac- tor of 105.

J. W. Ross (Orion): It really is, and I think if you go look at some of the

geological data on silicates and other very hard materials, you will find a very large variety of solubility products over the range listed, depending on whether it is freshly precipitated, aged precipitate or single-crystal

material. My second comment concerns the effect of hydroxide inter- ference on the lanthanum fluoride electrode and the fact that a showed a

time dependence. I expected a time dependence, of course, since the

hydroxide ion is entering the crystal lattice at a very slow rate, but I don't

know if I could estimate off-hand which direction that drift should be. It

is more complicated than just assuming that the hydroxide ion par-
418 ION-SELECTIVE ELECTRODES

ticipates in the charge-transfer process. The nature of the surface is continually changing, and it can go through all shades of gray from pure

lanthanum fluoride to lanthanum monohydroxy difluoride, dihydroxy,

and so on to pure lanthanum hydroxide on the surface. Since the nature of

the surface is changing, the nature of the ion exchange equilibrium constant must also be changing, and the drift could go either direction. My

final comment concerns the discouraging results you (Dr. Butler) had at high ionic strengths. This is a fact of life, I think, with the liquid ion

exchange electrodes. To be on the safe side, tenth molar is probably as high as you should go, although your use of the different internal filling

solutions is an elegant way to go still higher in some cases. However,

you do get charge transfer of anions and such things at these ionic

strengths.

Anonymous: On the lanthanum fluoride solubility product discrepancy,

I was wondering if the crystal structures were determined? Were they the

same?

J. W. Ross (Orion): Yes, the powder has exactly the same structure as the single crystal.

Anonymous: What methods were used to determine the solubility

products in the case of the lanthanum fluoride crystals?

J. W. Ross (Orion): In the case of the solubility product of the single

crystal, this was accomplished by equilibrating a lanthanum fluoride elec- trode with distilled water for several days and measuring the ambient

level of fluoride produced due to the solubility of the crystal, using the

electrode itself as the sensing device. In the case of the much higher value

of the solubility product that Lingane gives, this is determined by the titra- tion of fluoride by lanthanum nitrate and evaluated from the potential at the end point of the titration. Of course, the solubility product can be cal- culated from any point on the titration curve, but it is most convenient to do this at the equivalence point of the titration. This value obtained by

Lingane refers to the freshly precipitated lanthanum fluoride. In addition to this, there had been some thermal measurements by Powell and

Connick, I believe, at Berkeley several years ago. This again refers to the

finely divided precipitated material, and their values agree quite closely

with Lingane's. But again, it depends on the size of the crystal what the

solubility product will be, and an interesting problem would be to look at the single-crystal material, and I would expect that you would have dif- ferent solubility products for different faces of the crystal. A 1 1 1 cleavage

plane would probably be more or less soluble than a cleavage plane

parallel to the hexagonal axis. This may very well account for the ten- fold discrepancy between our value and Rechnitz' value both of which were obtained on single-crystal electrodes. But, in manufacturing the

electrodes, we make no attempt to reproduce the crystal orientation

of the crystal section, and this may be a reflection of that.
SYMPOSIUM DISCUSSION 419

R. de Levie (Georgetown University): I might add that we have had a

similar experience. We tried to measure the activity of lanthanum

perchlorate with the fluoride electrode and didn't get a constant potential.

The drift was not caused by the other (perchlorate) electrode. We did not form a precipitate, and apparently we cannot use the fluoride electrode as an electrode of the second kind.

J. N. Butler (Tyco): That's very interesting because Lingane's solubility

product measurements were made in a region where lanthanum ion was

present in excess, and there was equilibrium between the lanthanum ion

in excess and the precipitated lanthanum fluoride. E. J. King (Barnard College): While it is undoubtedly true that particle

size will have an effect on solubility and solubility product determinations, the freshly precipitated character also has a very striking effect, and

this is because of the non-equilibrium solid phase present. This is well

known in the familiar sulfides of qualitative analysis which have solubility

products that may be 1 0^ larger for the freshly precipitated particles as against the stable crystalline material, a factor of the same order of magnitude as you reported for lanthanum fluoride.

J. N. Butler (Tyco): This certainly is a possibility, but you would think

that, if the same crystalline forms existed for both the freshly precipitated

and the solid crystals, they would have much the same thermodynamic

properties. E. J. King (Barnard): I don't believe that they are the same crystalline

form.

J. N. Butler (Tyco): I have no evidence, and I am just going on what Dr. Ross has already stated. E. J. King (Barnard): If they do have the same crystalline form, the dif- ference may be in hydration. Gelatinous precipitates, such as the sulfides or aluminum hydroxide, do become much less soluble as they age without

necessarily undergoing any profound change in crystalline structure. Lanthanum fluoride may be exhibiting this behavior.

PANEL DISCUSSION (THURSDAY)

Anonymous: I understand that silicone rubber is a very generic term. Now, from the point of view of constructing electrodes, could we have some specific comments on what is meant by the term silicone rubber,

because I gathered that this makes a very great deal of difference.

J. W. Ross (Orion): I have had some experience with the silicone

rubber electrodes, but I am sure that Dr. Pungor would disagree with me,

and I may be biased, but I happen to opt for the solid-state variety. I honestly can't see any difference in mechanism between a heterogeneousimpregnated membrane and a solid-state membrane when you are talking
420 ION-SELECTIVE ELECTRODES

about such things as silver sulfide and the silver halides that are all good

ionic conductors. The silicone rubber membranes are made in such a way

that particle loading is high enough that you have particle-to-particle contact. The conduction process is the same, and the behavior of the elec- trodes should be virtually identical regardless of whether one is talking

about a single crystal or polycrystalline membrane or an impregnated

membrane. In my experience, though, the principle source of failure in electrodes in the case of the Orion electrodes, for example, is a failure of

the seal between the insulating barrel material and the actual membrane

material itself. In the case of the particle-impregnated membranes, I worry about the fact that there is a great surface interface present here

and a correspondingly greater chance for failure of seals. As far as the

matrix material goes, I don't think it makes any difference what kind of

silicone rubber you use or whether it's silicone rubber or not as long

as it makes a good seal to the actual conducting material.

J. D. Johnson f University of North Carolina): Since we generally must

use reference electrodes with liquid junction, we need to choose between

a porous-plug, fiber or sleeve type junction. Do we use a silver chloride or

a calomel electrode? Do we use saturated KCl, tenth normal KCl or nor- mal KCl in these electrodes? I realize that this question perhaps does not have an answer. But is there a best choice for a reference electrode when we standardize at one ionic strength and go out and measure at other ionic

strengths?

J. W. Ross (Orion): To go right down the line, and this is largely per- sonal taste on my part, I think silver chloride electrodes are better than

calomel electrodes because the temperature hysteresis problem is considerably less. I have had no experience with the Thalamid electrodes

which were discussed by Dr. Covington in his paper. With respect to the

junctions, I think that a sleeve-type junction is better than a ceramic-plug

junction which is better than a fiber-type junction. This is based mainly on

the fact that clogging problems are less serious when you have the larger flow. Now, what goes inside of that junction is again, I think, a matter of

taste within reason, and I think we have been wedded to saturated potassium chloride too long. For example, if one is making measurements in highly alkaline solutions, one might be better advised to use a potassium

hydroxide or sodium hydroxide solufion in the juncfion to try to eliminate

the contribution of hydroxide ion to the junction potential. Similarly, in acid solution, HCl might be a better choice than saturated KCl. If one is making measurements in very dilute solutions, one ought to be able to use

a somewhat more dilute filling solution, perhaps an equi-transferent mixture of potassium chloride-potassium nitrate. It is very hard to generalize,

and there probably isn't any one best solufion. One has to be reasonably

intelligent in choosing, depending on the particular problem one has in mind, and make a decision on that basis.
SYMPOSIUM DISCUSSION 421

J. N. Butler (Tyco): The thing that surprises me is that the Beckman

fiber-junction calomel electrode, that everybody carries around with his pH meter, has such really high reproducibihty. R. G. Bates (NBS): I would like to add to Dr. Ross' comments that I feel that we have been wedded too long to the saturated calomel electrode

and would like to put in a plug for using 3.5 molar KCl. I think that a lot of

the problems associated with saturated calomel electrodes arise when you

change the temperature and get the electrode plugged with KCl crystals.

As far as we can tell, the liquid junction potential is very much the same

at 3.5 molar as it is with saturated KCl. As for the choice between

calomel, silver chloride, and Thalamid, I think it depends a great deal on

the temperature range in which you are going to make measurements. The

calomel electrode is very unstable above 80 °C, but I think at room temperature the calomel is not too bad. The silver chloride is inclined to dis- solve in strong KCl solutions.

J. W. Ross (Orion): In getting away from saturated KCl with both the

calomel electrode and the silver-silver chloride electrode, the solubility of

the silver and the mercury in these solutions is quite large, approaching

10^3 or 10~4 molar. If one is making sulfide measurements, for example,

what one has is either silver or mercury sulfide precipitating in the junction, if one is using a single junction reference electrode. By going to more

dilute chloride filling solutions, the solubility of the silver or mercury goes

down dramatically, and one can get away from this problem.

J. N. Butler (Tyco): This is an especially important point in some

non-aqueous systems such as aprotic solvents like dimethyl sulfoxide and

dimethyl formamide. Here the solubility of silver chloride is approximately equal to the concentration of excess chloride so that it is quite essential to develop liquid junction potentials of the correct character or else to use

materials such as thallous chloride where the solubility is relatively low.

T. S. Light (Foxboro Company): I'd like to add some comments con- cerning reference electrodes. As already indicated, there is no one best

reference electrode. We have been working with electrode systems for a number of years, and receive many questions concerning trouble shooting

problems. We have come to the conclusion that between 50 and 90% of

the troubles are directly traceable to problems with the reference elec- trode. The process chemical industry has, by and large, standardized on

silver chloride reference electrodes. There are a number of reasons for

this. One is that when dealing with the food processing industry, the possibility of breakage might introduce contamination by toxic mercury or

calomel. In other industries, such as the photographic industry, mercury

vapors are objectionable, and calomel electrodes are not permitted in the

plant. Again, concerning reference electrode problems, difficulties may be

created for various other reasons. For example, sulfide, as cited by Dr. Ross, precipitates either silver sulfide or mercuric sulfide in the liquid
422 ION-SELECTIVE ELECTRODES

junction of a reference electrode, and these are two of the most insoluble

substances known. In effect the reference electrode has been made a measuring electrode for mercuric or silver ion. My advice if this happens is to throw the reference electrode away. It cannot be repaired, since the silver or mercuric sulfide cannot readily be dissolved and causes errors in the

liquid junction potential which are much greater than any of the standard

calculable liquid junction potentials that are known to exist with good

reference electrodes. The temperature coefficient also must be considered, and I am a strong advocate of the lower potassium chloride concentrations away from the saturation point, to avoid the problem of

crystallization in the liquid junction. As far as stirring is concerned, one

should find no effect on most cell emfs whether the solution is stirred or

not. If a stirring effect is obtained, there is a possibility that something is happening in the reference electrode junction. With a clean fresh junction,

stirring effects are seldom observed except for the liquid ion exchange

electrodes which have a different mechanism for cell potential. In this case, a steady stirring or flow rate is desirable.

G. D. Christian (University of Kentucky): Dr. Bates has pointed out the

advantage of using standards very close to the concentration of the un- known system to reduce the residual junction potential and for other

reasons. Do you visuahze a system whereby you can prepare a series of

standards over a range of concentrations using metal complexes of a pK

fairly close to the pM that you need? I can see many difficulties, but this would enable you to at least prepare some standards over a wide range of

concentrations especially for dilute solutions. R. G. Bates (NBS): To rephrase your question, you are asking whether

it is possible to visualize a series of metal buffers which would vary

greatly in metal ion activity and perhaps not vary greatly in ionic strength.

I think there is some hope for that, but I don't think we have the possibilities that we have with pH standards where there are weak acids of widely

varying pK. In some respects this would not solve the problem because

the liquid junction potential you wish to cancel out varies with the ionic

strength of your unknowns so widely that if you had a series of buffers of

0. 1 ionic strength it might not be very effective in nullifying the liquid

junction potential of your series of unknowns. I think this is an interesting

proposal, and it is one to which we have given some idle thought but

haven't been able to come up with any great series of possibilities which

would give us any useful plurality of metal buffers. W. C. Shaner (Sun Oil Company): Is it possible to use the electrodes,

such as the sulfide electrode, for measurements in non-aqueous systems

such as crude oil?

J. W. Ross (Orion): Yes and no. All of the solid-state electrodes function quite well in non-aqueous solvents provided the solvent does not at-
SYMPOSIUM DISCUSSION 423

tack the electrode barrel The electrode barrel is epoxy so that things like pyridine or nitrobenzene are not allowed, but methanol, acetone,

acetonitrile, and crude oil would be alright. However, in order to make the

measurement, you have to have some conductivity in the sample solution.

Otherwise, the resistance between the sensing electrode and the reference

electrode would be far too high. You would have many megohms floating

in the air and a good deal of noise generated. It would be possible to use

the electrode in crude oil if it were first diluted with something with a

fairly high dielectric constant such as methanol in fifty-fifty dilution. Then, provided one calibrates in that solvent background, one can get

honest ionic activity values. In fact, one of the recommended titrations of

fluoride is done in non-aqueous solvents.

S. H. Katz (Eastern Pennsylvania Psychiatric Institute): Dr. Butler,

you pointed out that sodium is a major interfering ion in the use of the cal- cium ion-selective electrode. I am very interested in the physiological ef- fect of this. Did you bother to calculate what the effect of the sodium ion

concentration is on the ambient calcium ion concentrations in the

physiological range? If you need those numbers, I'd say roughly 0.1 5M

sodium vs. 100-times less than that for calcium.

J. N. Butler (Tyco): I don't think you would get any interference in that range. Its only in very concentrated solutions that the selectivity begins

to fall off I believe that Dr. Moore knows much more about those ranges

than I do. E. W. Moore (Tufts University Medical School): Thank you Dr. Butler. The selectivity of the calcium electrodes in the physiologic concentration

ranges for Na+, K+, Mg++ and H+ has been carefully evaluated by Dr. Ross at Orion and also in our laboratory and our results agree rather

closely. This will be discussed in some detail in tomorrow's session. On

a mole basis, the selectivity for Ca++ over Na+ is about 10,000 to 1 , i.e.,

it requires about 10,000 times as much Na+ to generate a given electrode

potential. The selectivity for Ca++ over Mg++ is about 100 to 1. In serum

and other extracellular fluids containing 150 mM Na+ and 0.5-1.0 mM

Mg++, overall sodium and magnesium error is therefore believed to be

about +2% in apparent calcium ion concentration.

S. H. Katz (E. Pa. Psych. Inst.): May I ask a second question that is directed towards the standards concept? Has anyone decided upon or have suggestions for the use of standards for mixed ionic solutions such

as would be present in serum?

R. G. Bates (NBS): All I can say in reply is that this is in the second

phase of the program, so to speak, and the simple phase has to be decided

first. I think the activity of sodium and calcium in pure aqueous solutions

must be established by a convention before we can go to what will probably have to be secondary standards. When we get a series of prima-
424 ION-SELECTIVE ELECTRODES

ry standards that are satisfactory, then I think inevitably one will have to consider these standards for very important media such as isotonic saline, sea water and so on. Anonymous: I think I know the answer, and the answer should be no, but I want to make sure. Do you know of some specific electrode for chloride ions but for which bromide and iodide do not interfere at all, no

matter what the concentration?

J. W.Ross fOnoAzj: No!

End of First Discussion Session

FRIDAY MORNING SESSION

C. Pittinger (Vanderbilt University Hospital}'. Dr. Moore, you mentioned your apparatus and that of Orion using two different temperatures,

body temperature on yours and 25 °C on the Orion. What effect does the

12 °C or so difference have on the measurements?

E. W. Moore (Tufts): Binding of calcium to the serum proteins is tem- perature—dependent as well as pH-dependent. Loken and associates

have found by ultracentrifugation that free calcium (largely Ca++) is 10-12% higher at 12 °C than at 37 °C, suggesting that it would be 5-6%

higher with the Orion flow-through electrode at 25 °C than with our

static electrode at 37 °C. Comparison of serum Ca++ values with the two

types of electrodes must also include pH effects. Our static electrode

values were those at the original whole blood pH; flow-through Ca++ concentration values were those at the pH of serum after separation under

oil, about 0.08 pH units higher than blood pH. Both our data and those of

Loken indicate that this 0.08 pH increase would decrease the Ca++ concentration about 3-4%. The temperature and pH effects are therefore opposite in direction; Ca++ values with the flow-through electrode would be

expected to be about 2-3% higher than those with the static electrode. This is almost exactly the difference observed, with respective mean

Ca++ values of 1 . 1 6 mM and 1.12 mM.

FRIDAY AFTERNOON SESSION

A. Weisstuch (Betz Laboratories): I would like to know, in a continu- ous system such as cooling water or boiling water applications, what

would be the operational lifetime of an electrode, and what are the

problems with fouling?

T. S. Light (Foxboro): I would first like to mention that one should not

generalize about ion-selective electrodes; each has its own limitations and
SYMPOSIUM DISCUSSION 425

problems. For example, a calcium ion-selective electrode is an organic

liquid ion exchanger type and has an upper temperature limit of about

50 °C. As with pH measurements, familiarity with the system is desirable.

There are pH systems requiring very little standardization for months on

end. However good laboratory or plant operations suggest more frequent

checking. Standardization once a week is a reasonable frequency for

many applications. It is well known that pH electrodes may have coating

problems. In pubHc water supplies, reagents such as Calgon may be

added; and calcium phosphate then coats the pipeline and helps preserve

it; it also coats the electrode and interferes with the measurement. In this case, rinsing the electrodes with acid may be required once a week or even once a day. If a problem exists with coating on a pH monitoring

system, the same problem may exist with an ion-selective electrode

system. With the fluoride monitoring system, measuring at the one ppm

fluoride level, we have arbitrarily set up suggested standardization checks

for once a week. This is being safe and conservative. The electrode

systems seem to be stable because the temperature compensation is taken

care of, and these are reproducible reference electrode junctions because we can afford to keep the KCl flowing out fairly rapidly from the

reference electrode. In summary, I would say that experience dictates the

frequency of standardization. A. J. Panson (Westinghouse Research): I would like to point out another application, and this is the direct analysis of oxygen in the gas

stream. Apparatus is now commercially available which features soHd

electrolyte galvanic cells operated at high temperature, about 800 °C. Here the oxygen is measured in the gas phase with no need for scrubbing

or equilibration with a liquid phase. The oxygen reacts directly at a platinum electrode which is interfaced with a zirconia electrolyte. The

counter electrode is another platinum electrode on the other side of your

zirconia electrolyte referenced generally with air. Quite accurate analysis

of oxygen in the gas stream can be made in this way.

T. S. Light (Foxbow)'. This is a potentiometric measurement, not an amperometric measurement, is that correct?

A. J. Panson (Westinghouse): Yes, that is correct; it is a potentiometric

measurement. Quite accurate Nernstian response for a four electron reaction is observed. This system can be used for trace amounts of oxygen, for example, in inert gas atmospheres to be use in a processing furnace. Solid

electrolyte cells of this type have been used to measure oxygen activity in liquid sodium in heat transfer systems for fast breeder nuclear reactors. T. L. Bohl (Hays Corporation): I have a question concerning the alu- minum-iron complexation on the fluoride analysis of drinking water. To

what extent does this complex? For example, will 1 ppm aluminum complex 1 ppm fluoride, and what do you do practically when you're monitoring public water systems?
426 ION-SELECTIVE ELECTRODES

T. S. Light (Foxboro): As you mentioned, in public water supplies, the

two ions that pose a problem, for complexation of fluoride, are aluminum

and iron. Fortunately, however, the pH of pubHc water supplies is in the

range of 5 to 8. In this range, both aluminum and iron form insoluble

hydroxides, and the free iron and aluminum content is very low, a few

tenths of a ppm. But I also have a question. Suppose one does lose 2 or 3 percent of the fluoride present by complexation, what is desired in the

public health situation? Is it the free or the total fluoride? In the past,

analytical procedures have given total fluoride, but I have wondered if it isn't the free fluoride that is wanted. However, if the answer desired is total fluoride and the iron and aluminum present are not tied up by complexation with citrate or hydroxide, then some of the fluoride may be lost to the measurement.

T. L. Bohl (Hays): Although I am not completely conversant with this area, I believe that it is the total fluoride that is of interest, and it is my in- terpretation that this is because the public health people do not know

what use the water is going to be put to when it leaves the treatment plant.

Changes may occur that would release additional fluoride from the complexed state. PANEL DISCUSSION (FRIDAY)

J. E. Garvin (Northwestern University Medical School): First, I would

Hke to express my astonishment and joy at Dr. Moore's exposition, but I wonder if it would be possible, having had some small experience with

these, to inquire into a few of the details of the sample preparation and

conduct of the actual measurement. Our experience suggests that there

are a number of little tricks that make this marvelous output possible. E. W. Moore (Tufts): I would not say that there are any particular little tricks involved; it is more a matter of being extraordinarily careful all along the line — from sample collection to electrode fabrication. One

should be particularly careful to avoid pH changes in the sample, either

from loss of CO2 in preparation of serum or gain in CO2 from prolonged venous stasis.

J. E. Garyin (Northwestern Univ.): Do you take the tourniquet off then

and collect it from freely flowing blood?

E. W. Moore (Tufts): No, we usually leave the tourniquet on throughout

the collection, but it is only for a minute or so. Judging from the pH values

obtained in normals (venous pH 7.30-7.40) there does not appear to be

any significant venous stasis under these conditions. It should be

emphasized that the blood sample, once collected, is handled anaerobically, i.e., the blood is spun under oil, the serum is separated under oil and

again placed under oil. Some investigators have used Vacutainers for col- lecting blood, but we have not studied this specifically.
SYMPOSIUM DISCUSSION 427

J. N. Butler (Tyco): Could I make a comment in this connection? In

private discussions, it has come up several times that the geometric configuration of the interface between the liquid ion exchanger and the aque- ous solution makes a difference in the potential because of the electrostatic charge that this interface carries. Unless the calibration solution

and the test solution are measured under identical conditions of hydrostatic pressure and geometric structure of the interface, one may have

systematic errors of several millivolts resulting from this source, and I think this should be pointed out. E. W. Moore (Tufts): Yes, this was a problem with the first generation

electrode, i.e., those prepared with a Viscose cellulose membrane, and we

were careful to avoid differences in hydrostatic gradients between stan- dards and unknowns, i.e., the electrode was immersed to about the same

depth in all measurements. This does not appear to be a problem with the

flow-through system.

J. W. Ross (Orion): No, with the flow-through electrode, the geometry

is fixed so you are always guaranteed that you have identical conditions.

E. W. Moore (Tufts): There is a slight streaming potential with the

flow-through system, and it is advisable to obtain measurements in stan- dards and unknowns at identical flow rates.

J. W. Ross (Orion): There are flow rate problems with serum. At low

flow rates, one observes apparently less calcium in the sample than you

do at higher flow rates, although there is a plateau beyond which increasing the flow rate produces no further change. We have tentatively

identified this as loss of CO2 through the membrane itself and, with a fixed

sample of very small volume, this loss can become appreciable, but in a

flowing system above a minimum flow rate, there doesn't seem to be any

problem.

E. W. Moore (Tufts): Yes, I would add to that that approximately 75%

of the inquiries we get about these electrodes are situations in which people will put a series of standards in and get their curves, then put their serum in and notice that the whole standard curve has shifted. Whereas,

if you keep going back and forth between sample and standards, you will find that it is fairly stable for the rest of the day. It is just that first shock

that is troublesome. I don't think we really understand it yet, unless it is the CO2 as was mentioned by Dr. Ross. Anonymous: Do I understand you to mean that you put your standard

solution through, then you put the serum through, then you put another

standard through, and you maintain a continuous or repeated pattern so

that the electrode is, in a sense, repeatedly conditioned?

E. W. Moore (Tufts): Yes, exactly. The shift in the standard curve sometimes noted upon the first introduction of serum into the electrode

appears to us to be more or less random in its direction. Several investiga-
428 ION-SELECTIVE ELECTRODES

tors have told us that their electrodes tend to shift toward a more negative

millivolt reading upon the first introduction of serum. Because of this, we

have recently looked carefully at our last 6 months' data but could not determine anything systematic about it. There is no doubt, however, that something often happens when you first put serum into the electrode.

J. W. Ross (Orion): Another possibility is that it might have something

to do with the liquid junction as well. A liquid junction that has been ex- posed to serum may be somewhat different than one that has only seen pure aqueous solutions.

J. N. Butler (Tyco): It may also change the interfacial tension of the or- ganic-aqueous interface.

J. W. Ross (Orion): I would be surprised. The exchanger itself is quite

hydrophilic at the surface, that is, the surface is a surface-active agent. I would think its effect would swamp out any effect from the serum itself. F. Rothstein (Tufts University Medical School): I'd like to address

myself to the question of protein adsorption on surfaces. Those of us who have been in protein chemistry for many years are fully aware that proteins are extremely surface active and studies have indicated that if you take serum you will find, using the method of Langmuir and Blodgett

plus ellipsometry as the testing technique, that on hydrophilic surfaces

you will have protein multilayers being deposited from serum. Then, if you go to a hydrophobic surface, you will find other proteins also forming

multilayers. I would address myself to the problem of the nature of the

membrane in the case of the calcium electrode. I know for a fact that on

cellophane, for instance, you will have adsorbed protein on it unless you

really keep the solution moving over the surface. Some of the preliminary

work we've done in Dr. Moore's lab indicates to us at least that the

so-called conditioning might be a reflection of a weakly adsorbed

monolayer or multilayer on the membrane. I am very uncomfortable with

the ease with which this problem is being set aside. I think it is a very important problem not only of proteins but any surface active agent, and this problem should be under consideration. The second point. Dr. Ross, is it possible to use an Amicon membrane in this electrode because of the

rapidity of transport? My last point is the possibility of having in the

calcium flow-through system a pH electrode so that you simultaneously measure the pH and pCa.

J. W. Ross (Orion): Let me start with the last quesfion and work for- ward. Yes, there is no reason why you cannot put a flow-through capiliary pH electrode in series with the calcium flow-through system using the same reference electrode and two meters and determining both species

simultaneously. We have worked with the Amicon membrane. I assume

you're thinking of a device to keep the protein off the surface of the selective membrane or do you mean using it as a selective membrane itself? We
SYMPOSIUM DISCUSSION 429

have looked at a early type of Amicon membrane, but nothing recently. I understand they have a number of different types of membrane available now. With the early material we looked at, which we hoped would act much as a piece of cellulose dialysis membrane, we found that there was

residual selectivity in the Amicon membrane because of the presence of

unsatisfied charge sites which complicated matters for us. We have not in- vestigated beyond that point. Getting back to protein adsorption, maybe

it does take place; we can't say that it doesn't. If there is a protein layer on

the surface, it really should make no difference in the calcium reading of

the electrode, if we assume that the inside of that protein layer and the

outside are in equilibrium with the sample calcium activity. One could

conceive that it might slow down the time response of the electrode, however, we have not observed changes in time response on exposure to serum. If anything, the electrode responds faster to serum samples than

it does to aqueous solutions, probably because the serum sample is buffered with respect to calcium, whereas the aqueous calcium solution is not. As far as the so-called protein effects we were discussing, most of

these can be reproduced by using a bicarbonate-buffered calcium chloride

solution with no protein present. So, I am inclined to favor the theory that

this is a CO2 effect and not a protein effect, simply because it's a simpler

theory.

E. W. Moore (Tufts): I think you should emphasize that you are allowing for the presence of the calcium bicarbonate complex in your standard

calculations.

J. W. Ross (Orion): Yes, that is correct. Bicarbonate does form a modestly stable calcium complex.

E. W. Moore (Tufts): I might add. Dr. Ross, that the problems just al- luded to by Dr. Rothstein may apply to the second-generation calcium

electrode, i.e., the Model 92-20 static electrode marketed by Orion.

Although at least two papers have been published on the use of this elec- trode in serum, in our hands it was quite unsatisfactory. It generally gave

unstable potentials with more-or-less continuous drift in serum, although

it worked quite well in protein-free solutions. We assumed therefore that proteins were responsible for the drift, possibly through a coating of the

membrane, despite vigorous stirring. The behavior of this electrode there- fore appears to be quite different from that of the flow-through electrode. R. G. Bates (NBS): It occurs to me there might be quite a difference

between the protein error on a glass electrode and that on other types

of membrane materials such as lanthanum fluoride. Is this the case, Dr. Ross?

J. W. Ross (Orion): 1 don't know if anyone has looked at the lanthanum

fluoride electrode in protein solutions specifically for this effect, but my

guess is that the effect is probably very similar. Lanthanum fluoride is a
430 ION-SELECTIVE ELECTRODES

very polar surface. Fluoride ions on the surface are not entirely unlike the

oxide ions on the surface of a glass. I would think that anything bad that happens on glass might very well happen on the lanthanum fluoride

material as well. R. De Pablo (Diamond Shamrock Corporation) : I would like to know if you have studied the influence of thiosulfates and polysulfides on the sul- fide electrode.

J. W. Ross (Orion): Yes, we have looked at polysulfide formation, and

this occurs in samples from paper pulp plants which contain sulfide and a good deal of free sulfur from air oxidation. The sulfur stays in solution as polysulfide ions. The electrode only senses the free sulfide ion in equilibrium with these, and one could distinguished between them by a

direct measurement for free sulfide followed by a silver titration which

gives, in addition, the sulfide bound to the sulfur and you get polysulfides

in this way. You can also determine mercaptans by this technique as well. As far as thiosulfate that you mentioned, this ion has no effect on the sul- fide electrode. The silver-thiosulfate complex is not stable enough to cause any interference.

F. J. Tavora (Colorado School of Mines): I have a question for Dr.

Light. Concerning your differential cell, I wonder whether you could give

examples of other ions that could be determined with this arrangement or detected indirectly with the already existent ion-selective electrodes?

T. S. Light (Foxboro): Another example in addition to the determination of aluminum by measuring the loss of fluoride, would be the deter- mination of cyanide using as reagent an aluminum fluoride complex in which the fluoride is displaced by cyanide. The amount of fluoride dis- placed would be proportional to the cyanide activity. This might appear

to be an impractical example since a cyanide electrode also exists, but the

cyanide electrode is limited to dilute solutions. I think one can begin to have a lot of fun being chemically ingenious in this manner. For another

example, at the present time we do not have a good sulfate electrode, but

there is a good lead solid-state electrode. Using this lead membrane elec- trode and lead reagent solutions, the change in lead activity on one side of

the membrane would be a measure of the sulfate concentration. I think

you can begin to see how all of the analytical chemistry that we have

learned through the years can begin to be applied indirectly to using the

ion-selective electrodes and getting a lot of answers out of them.

T. R. S. Wilson (Woods Hole Oceanographic Institution): I wonder if anyone would care to speculate on the source of noise in electrode measurements? The reason I ask this is that I have been working with a dif- ferential type cell, such as the one that Dr. Light mentioned, which has no

liquid junctions, matched electrodes in good thermal contact, well ther- mally isolated and electrically shielded, and we can get noise levels down
SYMPOSIUM DISCUSSION 431

to below a microvolt. I wonder if anyone would care to apportion the

blame for the noise one sees with normal electrode systems between the

various possible sources.

T. S. Light (Foxboro): Am I to understand you correctly that you're

complaining about noises at the microvolt level?

T. R. S. Wilson (Woods Hole): I'm not complaining. It's taken a long

time to get to this level, and it is an illustration of the powerful nature of

the technique you mentioned, if you match your electrodes well and keep

them in good thermal contact.

J. N. Butler (Tyco): I would say that the most prevalent source of noise

is insufficient electrostatic shielding, particularly if you are in an area where there are a lot of RF machines melting things in other rooms, and

this RF noise makes it difficult to bring the dc noise level down because

you get rectification in all kinds of contacts. You have to use special sol- ders to bring these noise levels down. If you are working in a very high

impedance circuit, you can pick up enormous amounts of noise from ap- parently no source at all, simply the ac lines in the building even if you

build Faraday cages around your equipment.

T. R. S. Wilson (Woods Hole): May I just mention, in case someone is interested, that we are using a Keithley millimicrovolt meter to measure

these voltages, and we have to use electrodes of quite a large surface area because the input impedance is a little low on that meter. G. Eisenman (University of Chicago): What is the frequency spectrum

of this one microvolt noise?

T. R. S. Wilson (Woods Hole): We are using a chart display, and the

chatter on the record is on the order of one-tenth of a microvolt or less. There is a drift, which is not troublesome to us in our present application, on the order of microvolts per hour due to temperature changes in the room.

G. Eisenman (Univ. of Chicago): Well, I think that one general com- ment that may be made is that since the noise is not coherent then statisti- cal methods can reduce it as low as you want, if you have an infinite amount of time by which to reduce it. So in principle, it's not a problem.

T. S. Light ( Foxboro): As you may have gathered from my talk, I am in- vestigating the region below a tenth of a millivolt and, everytime we do

fight it down there, we find "noise," as you do, we go after it and try to clean it up. And lo and behold, we do clean it up after finding something to blame it on. We don't use statistical devices to get rid of it either. For example, I complained yesterday about reference electrodes

and noisy liquid junctions. You have raised the question of shielding.

I know there is an excellent article by Moore on shielding problems with

pH measuring assemblies. In the microvolt region, spurious signals

may be electrical measuring noise and have nothing to do with the
432 ION-SELECTIVE ELECTRODES

electrode systems. I honestly don't know how good electrodes are, but

I suspect they are inherently good in the microvolt region. One example

concerns shielding. Laboratory pH meters do have good shielding

but not completely adequate. On our instruments, we go to a concept

called a driven shield where the potential of the shield is maintained

at the potential of the inner wire. This cleans the signal considerably.

Someone already mentioned Faraday cages, these are all devices which

frequently solve measurement problems extraneous to the electrodes.

I am willing to go on record as saying that electrodes are able to go down

to the microvolt region. I believe they will obey the Nernst and other

equations better than generally believed now, and we're just arriving

at the stage of being able to prove it. J. R. Cels (Babcock and Wilcox Company): I would like to ask Dr.

Light about the working curves which were designed to go through zero

at the desired operating level of concentration, so that the shifts with temperature were minimized around that point. Would you elaborate on how

this was done?

T. S. Light (Foxboro): Yes, this is no great problem to elaborate on, and

I would first refer you to Dr. Bates' book on pH where the same concept

is treated. Most modern pH meters zero around a pH of 7, and this is ac- complished by having the internal filling solution of the measuring elec- trode, whether it is a pH electrode or a fluoride electrode, set to match the

solution concentration that is most common. For example, for the pH

electrode, the internal solution is buffered around a pH of 7. Two potentials dictate the internal of the measuring electrode, the solution inside

and the internal reference electrode which is usually either a silver-silver chloride electrode or a saturated calomel electrode. The internal potential

is set by the pH and the chloride concentration, and this chloride content

is matched to that of the external reference electrode. In the case of the

fluoride electrode, it becomes apparent then, when using a 1 molar potassium chloride reference electrode, one should have a 1 molar potassium

chloride internal filling solution in the fluoride electrode. The fluoride

electrode internal solution should also have a fluoride activity of 1 milli- gram of fluoride per liter of solution. Now, this electrode system immersed in a 1 milligram per liter fluoride solution will read zero emf. If the

temperature changes, the two silver-silver chloride reference electrodes

change in the same fashion so there is no net change in the emf. This is called the symmetrical cell concept and has been described in the pH

literature. R. G. Bates (NBS) : I should like to add just a word to that, if I might. I think that it is not quite sufficient to have a symmetrical cell because the

RT/F factor is going to change with temperature, and you want the pH to

nullify that change in order to maintain a zero standard potential. We've
SYMPOSIUM DISCUSSION 433

recently done some work in this area with regard to pH electrodes, but

unfortunately it is still not published. It is possible to choose the composition of the inner buffer solution so that its temperature coefficient is such

that it does nullify the E°. We found, for example, that a THAM buffer in a sodium chloride solution is a very good choice to nullify the E° of the

saturated calomel electrode.

T. S. Light (Foxboro): I guess I should have emphasized that the elec- trode has to be tailored to the particular measurement problem involved.

J. B. Dawson (S.U.N.Y.-Stony Brook): Could I add some medical

nitty-gritties to Dr. Moore's beautiful paper? Do you think the hyponatremia, which was not mentioned as one of the problems in cirrhosis,

makes any difference to your calcium readings? I presume the effect is probably pretty small and doesn't make any difference, but the sodium/potassium ratio is way out of whack in a cirrhotic and may be rele- vant. E. W. Moore (Tufts): There are several possible effects to be considered in Ca++ analysis in cirrhotics and also in other pathologic sera. The hyponatremia which you mentioned is associated with some reduction in serum osmolality, i.e., there is a reduction in total ionic strength.

This effect on calcium activity can probably be neglected, however, ex- cept in the most severe cases. Several years ago. Dr. Ross and I found

that the activity coefficient of CaCl2 in the presence of 1 50 mM NaCl was

about 0.54, as calculated from the observed mean NaCl activity (using a

sodium-selective glass electrode and Ag-AgCl electrode); at lOOmM

NaCl, the activity coefficient was about 0.58. Your second point concerning a change in the Na+/K+ ratio refers, I assume, to possible differences

in electrode selectivity for Na+ and K+. This can be entirely neglected I think, since the selectivity for these two ions is very similar, i.e., about

10,000/1 on a mole basis. A point perhaps more important is the level of Mg++ in the sample, since the selectivity for Ca++ over Mg^+ is only

50-100/1. We are hopeful that a suitable Mg++ electrode can be

developed; it would surely be a great boon to biology and medicine. The

questions which you have raised emphasize the difficulties encountered

by all clinical investigators — how does one apply a given finding or

regression equation obtained from data in a heterogeneous population

to a given individual?

J. B. Dawson (Stony Brook): May I just add one plea to this beautiful

technique of yours? Are you planning to do patients with long-term renal

failure? I am thinking in terms of Relman's buffer pool, buffering the

hyperacidity with the patient's body calcium. Are you doing any

long-term runs to see whether they're running a high ionized calcium

level? This would be a lovely group to look at. E. W. Moore (Tufts): Yes, we have just begun studies of renal dialysis
434 ION-SELECTIVE ELECTRODES

patients, to include the immunoassay of parathormone. I believe the

electrode will find particular usefulness in these patients. A. W. Meiseibach (DuPont): I noticed that a number of the electrodes

discussed today have a fair sensitivity to interference by ferric ion. Is it possible that we can get ferric measurements with some of the available

electrodes?

J. W. Ross (Orion): I think ferric ion is interfering with many of the

solid-state electrodes because it is a fairly good oxidizing agent. I don't

think there's much chance of using these electrodes for determining the

ferric ion. This is quite an irreproducible effect.

J. N. Butler (Tyco): I can also add that, at the Gordon Conference in Santa Barbara last week, Isaac Tractenberg of Texas Instruments

described some electrodes he had made using some complex selenium

glasses of undefined composition which he said were specific to iron in aqueous solution, but I'll have to refer you to him for details. R. P. Buck (University of North Carolina): In the determination of lead or copper, I was wondering if I could use the silver sulfide electrode but,

prior to that use, I could take powdered copper sulfide or powdered lead

sulfide and stir it up in my solution? My second question has to do with the use of the silver sulfide electrode in extreme conditions. A good deal was

said about the use of the silver sulfide electrode when the sulfide activity was as low as lO-^^ molar. That doesn't bother me so much because, in those circumstances, if equilibrium prevails, a large number of silver ions are present. It's the silver ions that make the difference. What's incredible

about the silver sulfide electrode is that it operates in one molar sulfide —

one molar hydroxide solution where there is a very low silver ion activity.

Would you comment on that, and do you have any feeling for what

goes on at the surface of these solids in conditions of low electrolyte concentrations in general?

J. W. Ross (Orion): Yes, one could use a silver sulfide electrode for

doing a copper analysis by throwing in some powdered copper sulfide which, by a direct reaction, gives an equivalent release of silver. This

idea works very well on paper and, in fact, this is what lead us to the use

of the mixed-precipitate membranes to make use of this same effect. In

practice, it doesn't work too well, particularly at low concentrations,

because you're putting in a huge surface-area precipitate. The ions that are released are, for the most part, adsorbed on the surface of this precipitate and are not available in solution for the electrode to measure. At high concentrations, it would work quite well, again, if one were

willing to wait for the reaction to complete itself which may take some

time since it involves a solid phase. We've done a Httle work on the use of

the silver sulfide electrode at low concentrations recently. In principle,

with these very insoluble sulfide membranes, one should be able to go
SYMPOSIUM DISCUSSION 435

down to something like IO-20 molar. What really does determined the

lower level of measurement is inevitably something on the order of 1 0-^

molar, very rarely lower than that. My current view, which is based on a very limited number of measurements, indicates we are limited by ion ad- sorption on the surface of the electrode itself. It is a well known fact that any crystal surface will selectively adsorb common ions from solution

onto the surface. So if one starts out with the best distilled water one can

get, puts a silver sulfide electrode in it, and then starts adding small incre- ments of silver ion, one finds that the first increments that you add all wind up adsorbed on the surface of the electrode and are not available in solution for the electrode to sense as the free ion activity. In general, the

larger the electrode surface area, the worse this problem becomes, which

again leads me to the assumption that it is adsorption on the crystal sur- face itself. This is much the same for all the silver salt electrodes.

J. N. Butler (Tyco): I might also add that even thermodynamically

speaking, although you may be sensing 10-^5 moles per liter sulfide ion,

the mechanism may proceed through a complex and still give the same

thermodynamic potential as it would have had the mechanism proceeded

through the sulfide ion itself. J. W. Ross (Orion): Right, you are not asking to have a large number of

the ions you're trying to measure at the surface. What you're asking is that you have mobile equilibria that can produce this very low fixed level at a

rapid enough rate to stay ahead of any interfering reactions, and this does seem to be the case for the silver sulfide equilibrium which is quite rapid

and mobile.

Anonymous: I would like Drs. Light and Ross to thrash something out. Dr. Light, when talking about the practical applications of these elec- trodes, talked about using n electrodes, all of which experience inter- ferences, then correlating the results to get the n correct answers. On the

other hand. Dr. Ross seems to almost dismiss the idea of using selectivity

factors in this way. I was wondering, where is the truth? Somewhere

in the middle?

T. S. Light (Foxhoro): In order to make this correction with some kind

of a signal processor or computer, you have to have equations and be able

to solve them. This is my starting premise. Now, some selectivity coeffi- cients have been indicated to be quite valid and reproducible. I believe Dr. Ross cited an example of a selectivity coefficient that changed as the

composition changed and, if this is so, then the equation wouldn't be

satisfactory.

J. W. Ross (Orion): I am very disenchanted with the idea of correcting an electrode which is experiencing an interference to remove the effect of

that interference. Yes, one can always develop a more complicated equation with more parameters to fit the data and perhaps to get a better cor-
436 ION-SELECTIVE ELECTRODES

rection, except for the fact that it has been my experience that electrodes

that are undergoing interference have other problems. They have slow,

drifting responses, and time dependent phenomena of this sort would be

awfully hard to handle. Other types of computation, however, are valid,

and I think doing computations makes a great deal of sense in this situation. Suppose you have a sample where you trying to measure fluoride or

sulfide or some other ion whose free ion activity is pH dependent, and

you want to know both the free ion concentration and the total concentration. In this case, it is quite possible to independently measure pH, the pH

electrode being another electrode in this string of n electrodes, and go

through magnificient calculations to get all of the separate species out of

this. These are perfectly valid equations because you are doing computations relating to species in chemical equilibria in the solution, and it has

nothing to do with the electrode interference. Here, I think this ability of

being able to do extensive computations makes a great deal of sense. But,

with the liquid electrodes when they are experiencing interference of

something entering the membrane, those potential values, in my view, just

aren't to be trusted. With the solid electrodes, as I pointed out in my talk,

the interference effect is different. In the usual situation, there is either no

interference or the electrode isn't working. You are over that abrupt fall off onto some other function and here a calculation makes no sense whatsoever. A. K. Covington (University of Newcastle upon Tyne): I think the answer is to get the solution to the right state before the electrode sees it, by addition of another reagent, maybe just changing the pH or something

much more complicated. But we should utilize these ion-selective elec- trodes knowing their limitations to get the process stream right before the

electrode sees it. J. N. Butler (Tyco): I might underscore something that I said in my talk yesterday which was that, although the selectivity ratio is a useful qualitative concept for solid-state and liquid ion exchange electrodes, it does not have the quantitative significance that it does with the glass electrodes.

Especially in concentrated solutions, it may change by several orders of

magnitude as you change the solution composition. This is something to keep in mind.

End of Symposium
INDEX

Accessibility windows, 317 Accuracy of calcium electrode measurements, 241 measurement, 355

Acetate, electrode response to, 409

Acid-base reactions, equilibrium constants

for, 146

Acidity effects, fluoride electrode, 156

Activity, 143, 317

and concentration, 357

calcium ion, 224

cation, 3 conventions for, 197

intracellular, 296

iodide in iodinated proteins, 309

ionic, 191, 196, 287, 295, 296

single ion, 191 standards for ion-selective electrodes,

191

zinc chloride, 147

Activity coefficients. 111, 143, 357

calcium chloride, 182 calcium fluoride, 433

calcium ion, 224, 242, 244

fluoride ion, 159, 162

hydrochloric acid, 145 measurements, 171

single ion, 149, 182, 199 sodium fluoride, 161, 171, 172 sodium fluoride, salting-out effect, 152

Activity measurements, calcium ion, 185

Activity scale, calcium ion, 224

Addition techniques, 381 Adsorption on electrode surface, ionic, 434

protein, 428

silver, 177 Advantages of silver sulfide membrane

electrode, 177

Affinities as a function of chemical composition, 28

Agricultural samples, boron in, 398

Agricultural analysis and pollution control,

nitrate electrodes, 397

Air, determination of water soluble fluoride, 392

Air pollution, fluoride, 392

Albumin, 226, 259, 261 and globulin, relative binding of calcium, 278

binding constant, 278 bound calcium, 264

level, serum, 268, 274

molecule sites, 247

relation of total calcium to protein-bound

calcium, 261

serum, 234, 257

Alkali halide, crystal lattice, 30

Alkali metal cations, glass electrode, 2 Alkali metal ions, precipitation with tetra- phenylboron, 331

Alkaline earth cations, glass electrode, 2 Aluminum

and iron, complexation of fluoride, 425

differential analysis cell, 369

fluoride ion reaction with, 337

in Bayer liquor, determination, 370 Amalgam electrode, calcium, 216 Amalgam electrodes, 125, 148 Amberlite in polystyrene matrix, 90 Amicon membrane, 428

Analate additions potentiometry, 384, 385

Analyses

extracellular, 295

intracellular, 296

laboratory, 375

Analysis and control, industrial, 349

boron, 398

chemical, 342

continuous, 349

differential, 367

differential analysis cell for aluminum,

369

effluent streams, 349

fluoride ion in water supplies, 360

microelectrode, 287

on-line, 349

solid electrolyte galvanic cells for oxygen

in gas streams, 425

process, 349

titration, 366

Analytical expressions for glass electrode

potential, 2 Analytical instruments, industrial, 359437
438 INDEX

Analytical studies on electrodes, 313

Analytical study of silver sulfide electrode, 406

Anion, organophilic, 4

Anionic field strength and selectivity, 30

Anion-selective

liquid membrane electrode, 16, 328

liquid systems, 72

nitrobenzene membrane electrode, 16

Antibiotics, 21

cyclic, 1 macrocyclic, 32

neutral macrocyclic, 7 Antimony electrode, 307

Applications

biomedical, 215, 298

industrial monitoring, 371

of ion-selective electrodes, 375, 388

pollution monitoring, 371 Associated liquid ion exchangers, selectivity parameters, 10 Associated pairs, 44

Association between counterion and site, 16 constant for neutral pairs formation, 5 constants, 6, 18, 54

limiting case (strong), 5

strong, 49 Asymmetry potential, 114, 149

Available electrodes, 350 Barium sulfate heterogeneous membrane electrode, 95,

101

paraffin membrane, 93 Bayer liquor, determination of aluminum,

370

Beer, determination of calcium, 396

Behavior

n-type, non-ideal, 37

pseudo-Nernstian, 144

sodium-sensitive glass electrode in fluoride solution, 171 Benzoate, electrode response, 409

Bias potential, 1 14, 116

Bicarbonate, calcium complex, 224, 429

Bilayer membranes, 24

Binding energy, 34

Binding constant albumin, 278

globulin, 278

Binding of calcium to serum proteins, 222,

243, 282, 424

Bioelectrodes, 293

Biologic and medical importance of fluoride, 308

Biologic fluids, calcium in, 215, 395

Biologic measurements

in vitro, 293

in vivo, 293

Biologic membranes, 1,31

cation discrimination, 36

potential, 293

Biologic solutions, 289

Biologic standards, 292

Biologic systems

direct measurement of ionic activity, 287

flowing, 295

non-flowing, 295

Biomedical applications, 215, 298

Biomedical research, 287

Bis-2-ethylhexyl phosphoric acid, 7, 18 Bismuth phosphate impregnated electrode, 101 Bjerrum plot, 321 Black liquor, 361 Blood

calcium, 239, 426

cerebrospinal fluid barrier, 247

sampling of calcium, 426

Bone, fluoride in, 308, 391

Boride redox electrodes, 94 Born-Lande equation, 30 Born repulsion energy, 30 Boron

analysis of, 398

in agricultural samples, 398 Boundary conditions, 42, 48 Boundary equilibria, velocity of establishing, 42 Boundary, membrane-solution, 40

Bridging electrodes, reference electrodes

as. 111 Bromide, 1 16

electrode response to, 409

electrodes, 78, 400

titration of, 40

1

Bromide electrode, epoxy equivalents by, 400

Buffer

for determination of fluoride, 153

ionic strength, 415

total ionic strength adjustment, 359, 380
INDEX 439

Cadmium, 80

ion-selective electrodes, 407

titration with EDTA, 81

Calcitonin, 216

Calcium, 93, 103, 423 amalgam electrode, 216

analysis in cirrhotics, 433

analysis in pathologic sera, 433

bicarbonate, 224, 238, 429

binding ability of protein polysaccharides

of cartilage, 3 10 binding to serum proteins, 243, 282, 424

blood sampling, 426

chelates, 218

chelation with nitrilotriacetic acid, 185, 328

citrate complex, 238, 328

complexes, 185, 218, 239, 254 complex of phosphate, 238

continuous monitoring, 221 DCTA complex, 328

diffusible complexes, 237, 254

diffusible complexes of normal serum, 237

dissociation constant of protein-bound, 242 EDTA complex, 328

effect of hyponatremia, 433

electrode evaluation of therapy, 253

flow-through electrode, 221, 427

fractionation of protein-bound, 278

fractions of serum, 243, 254, 269

globulin-bound, 264

heparin complex, 240

in beer, 396

in biologic fluids, 395

in gastric juice, 223

in sea water, 397

in serum, 217, 253, 281, 395

in skim milk, 397

in spinal fluid, 249

ion activity, 224

coefficients, 224, 242, 244

measurements, 185

scale, 224

ionized, 216, 217, 221, 234, 254, 257

ionized and serum total, 234, 257

ion-selective electrode, selectivity of calcium over magnesium, 423

lactate complex, 238

level in renal dialysis patients, 433

Calcium — Continued

levels of protein-bound, 243

liquid ion-exchange electrode, 183, 309, 395

malate complex, 328 nomogram for protein-bound, 261, 265

on-line monitoring, 283 pH dependence of ionized, 225

phosphate complexes, 224

phosphate ester systems, 65

physiologic importance, 216

precipitation of complexes, 239

protein-bound, 218, 254, 259, 261, 268, 270

protein interaction, 247

relative binding to albumin and globulin, 278 serum ionized and total, 230, 233

solid ion-exchange electrode, 395

streaming potential with flow-through

electrode, 427

studies of complexes, 185

studies of hypercalcemia of cancer, 269

study of EDTA reaction, 395, 416

sulfate complex, 238

temperature dependence of binding to serum proteins, 222

titration of fluoride, 390

titration with EDTA, 226, 395, 416

titration with EGTA, 397

ultrafiltrable, 235, 254

Calcium-albuminate, dissociation constant, 244

Calcium carbonate, 239

Calcium chloride, mean activity coefficient, 182 Calcium citrate, dissociation constant, 228 Calcium didecylphosphate, 180 Calcium electrode, 202, 206, 222, 233, 411, 429

accuracy of measurements, 241

biomedical applications, 215

calibration, 224

characteristics, 219

characteristics of flow-through, 221

clinical applications, 215 computer interfacing, 225

flow-through, 221, 427

hydrogen ion and potassium ion errors, 223 hydrogen ion interference, 66
440 INDEX

Calcium e\ectro6e— Continued

interference by sodium and magnesium,

223 pH effect, 182, 231

poisoning by protein, 244

response time, 183

selectivity for calcium over magnesium,

423, 433

selectivity for calcium over sodium, 423

selectivity ratio, 183 sodium ion interference, 68

solid organic matrix, 185

static, 219

temperature effect, 231 Calcium fluoride, ,433 Calcium fluoride, solubility product of, 168 Calcium oxalate, heterogeneous membrane

electrode, 93 Calcium oxalate, paraffin electrode, 93

Calcium-proteinate, dissociation, 242 Calcium stearate electrode, 93 Calcium sulfate dihydrate, solubility product, 185

Calibrating standards, 292

Calibration calcium electrode, 224

curves, 379

electrode, 380

Calomel

disproportionation of, 118

electrode, 1 12, 1 13, 118, 122, 421

electrode, temperature hysteresis, 1 18 Cancer, calcium electrode studies, 269

Carbide electrodes, redox, 94 Carbon dioxide effect, 429 Carbon dioxide losses from prolonged venous stasis, 426

Carboxylate ion exchanger, 16 Carriers of ions, molecular, 7 Cation, 21

activity, 3 analysis using sodium and potassium

electrodes, 364

discrimination by biological membranes,

36

effectiveness, sequences, 31 exchange, 314

exchange membranes, glass, 2

mobility, 2, 314

permeation mechanism, 7 Cation-sensitive glass electrode, 148

Cation-site interaction, free energies of, 30

Cell reactions, 192

Cell, symmetrical, 432

Cell without liquid junction, 145 Cellophane membrane, 93

Cellular physiology, 296

Cellulose dialysis membrane material, 62

Cerebrospinal fluid active transport into, 249

electrochemical equilibrium of calcium, 250

facilitated transport into, 249

Characteristics of flow-through calcium

electrode, 221 Charged complexes, mobilities of, 53, 54

Chelates

calcium, 218

metal, 90

Chelating titrations, 228

Chemical analysis, 342 Chemical and biochemical kinetics, 330

Chemical composition, affinities as a funcfion of, 28 Chemical coupling within membranes, 43 Chemical nature of lipophilic ion exchanger,

18 Chemical nature of liquid exchanger, 6 Chemical potenfial, 37 Chemical properties of lipophilic ion ex- changer molecules, 16, 18 Chemical properties of site, 18 Chloride, combinafion electrode, 400

Chloride electrode, 78, 90, 95, 111, 115,

1 16, 1 18, 124, 134, 146, 202, 203, 306, 400, 409

Chloride ion interference, fluoride elec- trode, 416

Circulafing fluids, continuous monitoring, 295

Cirrhosis

effect of hyponatremia on calcium level, 433 serum calcium, 253

sodium/ potassium ratio, 433

Cirrhotics, calcium analysis, 433

Citrate, calcium complex, 238, 328

Classification of reference electrodes, 108

Clinical applications, calcium electrodes, 215

Co-ion exclusion, 50

Collodion matrix, 90

Collodion membrane electrodes, 217

Colloidal polyelectrolytes, 287
INDEX 441

Colloidal solutions, 289

Combination electrode for chloride, 400

Complexation of fluoride with aluminum

and iron, 425

Complexed-cations

charge of, 10

size of, 10 Complexed species, total concentration, 383 Complexes, 144, 317

calcium, 185, 218, 239, 240, 254, 270

calcium bicarbonate, 224, 238, 429

calcium phosphate, 224, 238

copper, 327

fluoride, 163, 164, 165, 168, 169, 369

formation constant of, 319

ionic, 52

mobile charged, 7

mobilities of, 53, 54 monofluoroaluminum, 324

positively charged lipid-soluble, 24

precipitation of calcium, 239

silver chloride, 146

stoichiometry, 21, 319 Complex studies with liquid membrane

electrodes, 327 Components of serum total calcium, 235 Composition of glass, 314

Computations relating to species in chemical equilibria, 436 Computer interfacing with calcium elec- trode, 225

Concentration and activity, 357

cell, 376

free ion, 357

free sites, 48

gradients, diffusion, 40

hysteresis, 108

total ion, 357

Condition of electroneutrality, 49

Conductances, single ion, 18 Constant ionic medium, 147, 149

Constants, 6

ion exchange equilibrium, 10

selectivity, 69, 97, 99 Continuous analysis, 349

Continuous flow system, 331 Continuous monitoring

ionic activity in circulating fluids, 295

ionized calcium, 221 Continuous systems

Continuous systems — Continued

operational lifetime, 424

standardization frequency, 425

Control, industrial, 349

Convective mixing, 50

Conventions for ion activity, 197 Coordination number of ligands, 32 Copper complexes, 186, 327

Copper-selective electrode, 72, 80, 84 Coulomb's law, 28

Counterion, 42, 44

Crystal lattice, alkali halides, 30

Cupric hydroxide, 317

Cupric ion-selective electrode, 327, 407

Curie principle, 44

Current, 46, 48

electronic contribution to, 38

exchange, 108 Curves, calibration, 379

Cyanide, 84

determination of, 430

ion-selective electrode, 364

pollution monitoring, 367 Cyanide electrode, study of metal ion complexes, 402

Cyclic antibiotics, 1 Cyclic polyethers, 7, 21, 36

Cystic fibrosis screening, 400

Debye-Hiickel convention, 210 Debye-Huckel theory, 149, 174 Debye length of membrane phase, 52 Deep sea monitoring, 393

Definition of ion activity, 61 Degree of dissociation, 48 Deuterium gas electrode, 1 10 Development of liquid membrane systems, 64 Development of heterogeneous membrane

electrodes, 89 Dianemycin, 36 Dichromate, perchlorate electrode response

to, 399

Dicyclohexyl-8-crown-6, 21

Dielectric constant of solvents, 5 Differential analysis

cell for aluminum analysis, 369

using reagent addition, 367

Differential cell, 430

Diffusible calcium complexes, 254, 270

Diffusible complexes, relative values for ionized calcium and protein-bound

calcium, 270
442 INDEX

Diffusion concentration gradients, 40

Diffusion potential, 37, 40, 42, 127, 135 Dimethyl sulfoxide, fluoride electrode in, 176 Dioctylphenylphosphonate, 180

Dipolar sites, 27

Direct comparison of reference electrodes with ion-selective electrode, 1 10 Direct emf measurements, 384

Direct measurement of ionic activity in biological systems, 287

Direct potentiometry, 375, 388

Disproportionation of calomel, 118

Dissociated ions, mobility, 5 Dissociated ion species, partition coeffi- cient ratio, 6

Dissociated liquid ion exchangers, selectivity parameters, 10

Dissociation constant calcium-albuminate, 244

calcium citrate, 228

calcium-proteinate, 242

calcium sulfate complex, 185 protein-bound calcium, 247

Dissociation degree of, 48

limiting case of complete, 5, 49

Distribution coefficients, 18 Divalent cation electrode measurement of magnesium in sea

water, 406

water hardness measurements, 406

Divalent cafions, liquid ion exchanger for, 1 Dodecylamine, 16 Donnan equilibria, 2 Double liquid junction, 130

Drift, electrode, 60

Driven shield, 432 Dry glass, 3 EDTA

exchange of calcium and magnesium, 185

infusion of di-sodium, 252

titration of cadmium, 8

1

fitration of calcium, 395, 416

total calcium by titration, 226

Effect of geometric configuration on the electrode-solution interface, 427

Effect of hyponatremia on calcium level

in cirrhosis, 433

Effect of serum on liquid-juncfion, 428

Effluent streams, analysis, 349 EGTA titration of calcium, 397

Electrochemical potential gradient, 37

Electrode, 81, 109, 145, 193

activity standards, 191 amalgam, 125, 148, 216

analyfical techniques, 375

anion-selective, liquid membrane, 16, 328

antimony, 307

bromide, 78, 400, 409 cadmium, 80, 407

calcium, 66, 68, 180, 182, 183, 185, 202, 206, 215, 216, 219, 221, 222,

223, 224, 225, 231, 244, 253, 269,

309, 395, 41 1 , 423, 427, 429, 433

calcium amalgam, 216

calcium oxalate, 93

calcium stearate, 93

calibration, 224, 380

calomel, 112, 1 13, 118, 122,421

chloride, 73, 78, 90, 124, 134, 202, 203, 400, 409

classification of reference, 108

collodion membrane, 217

copper, 80, 84, 407, 434

cyanide, 84, 364, 401

deuterium gas, 1 10

diagnostic tool in the characterization of reaction mechanisms, 340

divalent cation, 406

drift, 60

effect of radiation levels on hetero- geneous iodide, 401

ferric ion, 434

flow-through, 221, 427

fluoride, 75, 84, 102, 148, 149, 150, 152, 153, 154, 155, 156, 157, 159, 171, 173, 174, 176, 186, 202, 208,

308, 319, 400, 411, 417, 418

fluoroborate, 73, 398

formate, 409

fouling problems, 424

glass, 2, 11, 16, 30,42, 110, 111, 124, 136, 147, 148, 171, 173, 193, 205, 212,

217, 298, 299, 300, 313

heterogeneous membrane, 89, 90, 93, 94, 95, 99, 100, 408

hydrogen, 1 6, 90, 1 1 0, 1 1 1

, 1 1 4, 299

incompletely sealed micropipette, 299

interferences, 66, 68, 173, 223, 353, 417

iodide, 78, 309, 400, 401, 409

ion-association extraction systems, 409

kinefic response, 155

lead, 72, 80, 407, 408, 430, 434
INDEX 443

Electrode — Continued

liquid ion-exchange, 50, 94, 180, 185, 309, 415

lithium, 16 macrotetrolide, 409

measurements in non-aqueous systems, 422

mercury-mercurous

acetate, 123 benzoate, 124

carboxylate, 123

chloride, 118

oxalate, 123

picrate, 1 12 propionate, 124

sulfate, 122

metallic, 306

nickel, 90, 93

nitrate, 73, 397, 409, 412

noise, 430

nonactin homolog, 409

non-glass, 306

n-type, glass, 2 oxalate, 93, 409

oxidation-reduction, 307, 361 oxygen, 425

perchlorate, 73, 328, 399, 409

performance tests for, 1 95

phosphate, 101 potassium, 1 1, 90, 304, 364, 409

potential, 1, 2, 6, 191, 192, 225

precision, 60

properties of systems, 94

protein adsorption on surfaces, 428

protein poisoning, 290

p-toluenesulfonate, 409

quinhydrone, 307

redox, 94

reference, 95, 107, 108, 110, 111, 11 113, 194, 203, 420, 421

response, 191, 409

response time, 155, 183, 295

salicylate, 409

selectivities of glass, 30

silver, 16, 77, 146

silver-silver bromide, 1 17

chloride, 111, 115, 1 16, 306

halide, 115, 399

iodide, 117

sulfide, 101, 179

silver sulfide, 177, 179, 324, 402, 40^ 411,412,413,434

E\ectro6e— Continued

sodium, 16, 1 12, 173, 202, 205, 217, 303, 354, 364, 366

source of failure, 420

stability characteristics of glass, 16

stirring effect, 154, 422

stirring effects on reference, 422

streaming potential with calcium flow- through, 427

sulfate, 90, 101, 122, 409

sulfide, 77, 101, 353, 402, 405, 413, 430

tetraalkyl ammonium chloride, 73 Thalamid, 124

thallium amalgam-thallous chloride, 124, 134

thiocyanate, 78, 408, 409

water hardness, 360, 406

zinc, 90

Electrode methods, advantages and dis- advantages, 60

Electrode potential, analytical expressions

for glass, 2 Electrode-solution interface, effect of geo- metric configuration, 427

Electrode surface, ion adsorption, 434

Electrode systems, solvent extraction, 408

Electrodes, multiple ion-selective, 364

Electrodes of the second kind, 145

Electroneutrality, 25, 43

Electrostatic field strength, 28

Electrostatic model of site, 27

Energy, binding, 34 Epoxy equivalents, 400

Equations, Planck and Henderson, 133

Equilibria

computations, 436 Donnan, 2 hydrofluoric acid, 157

oxidation-reduction, 143 Equilibrium constants, 25, 40

acid-base, 146

ion exchange, 10 Equilibrium selectivity, 27

Equilibrium specificity, 27

Equilibrium studies, 163, 313

Equilibrium, thermodynamic, 40

Equivalence point of potentiometric titra- tions, 386

Equivalence-point potential, 386

Errors in electrode potential, 225 Europium, 148 Europium fluoride, solubility product of, 166
444 INDEX

Exchange current. 108 Exchange of calcium and magnesium with EDTA, 185 Exchangers, 3

1

liquid ion, 1.16

selectivity of liquid ion, 1 selectivity of solid ion. 1 solid ion. 1 Extracellular analyses, 295

Extracellular biologic systems, flowing, 295

Extraction, salt, 25

Facilitated transport into cerebrospinal

fluid, 249

Factors determining selectivity, 10, 26

Ferric ion

electrode. 434

fluoride complexes. 168

interference. 434

Filling solutions, reference electrode, 421 Fixed monovalent sites, 37

Fixed-site ion-exchange membrane, 313 Flow rate problems with serum. 427 Flow system, continuous, 331 Flow-through electrode, calcium, 221, 427

Flowing extracellular biologic systems, 295 Flowing liquid junction, 128 Flowing samples, 314

Fluoride. 103, 389

acidity effects, 156

activity coefficient, 152, 162. 171, 172

air pollution, 392 aluminum and iron complexation. 425 aluminum complex. 369

biologic and medical importance. 308

complexes. 163. 164, 165, 168. 169

detection limit. 84

direct potentiometric determination, 390

effect of hydrogen peroxide, 152

electrochemically generated, 385

electrode. 75. 84. 102, 149, 150, 152, 153.

154, 155, 156, 157, 159, 171, 173,

174, 176, 186, 203, 208, 308. 319. 400. 41

1

equilibria. 163, 166

equilibrium studies, 163 hydroxide interference, 417

in air, 392

in bone, 308, 391

in calcifications, 392

in dimethyl sulfoxide, 176

in human saliva, 308

in non-aqueous solutions, 422

Fluoride — Continued

in toothpastes, 390

in water supplies, 360

iron complexes, 323

kinetic studies, 174 lanthanum, 75, 102, 148, 159, 163, 429

lanthanum response of electrode, 418

metallic ion interferences, 152

monitor. 361 monitoring of stack gas effluents. 367

monitoring of water systems, 425

non-ionic materials effect, 152 phosphoric acid buffer. 153

pollution monitoring, 367

precision of measurement, 159

protonation of, 163

reproducibility, 154

response, 94

response time, 155

selectivity of electrode, 154

silicate interference, 150

specificity test, 153 standard addition technique, 383, 390

stannous complexes, 168

titration of lithium, 176. 388

titration with lanthanum, thorium and

calcium, 390

Fluoride to chlorinity ratio in sea water, 393

Fluoride in organic compounds, 394

Fluoroborate

electrode, 398

formation, 398

hydrolysis, 169

Fluosilicate ion, 169 Flux equations, 2, 42

Forces and fluxes, 44

Formate, electrode response, 409

Fouling problems with electrodes, 424

Fractionation of protein-bound calcium, 278

Free diffusion liquid junction, 128 Free energies of cation-site interaction, 30

Free energy of hydration, 27 Free sites, 48

Future developments, 86 Galvani potential, 191 Galvanic cell for analysis of oxygen in gas

streams, 425

Galvanic cells, 191 Gas stream monitoring, 367 Gaseous pollutant monitoring, 367

Gastric juice, calcium, 223 Gibbs-Duhem relation, 173
INDEX 445

Glass

cation exchange membranes, 2 composition, 3,314

dry, 3 hydrated layer, 3,314

insulation, 297

Glass-to-glass seal, 301

Globulin, 226, 259

binding constant, 278

serum, 257

Globulin-bound calcium, 264

Gradient, potential, 37, 46

Graphite electrode redox, 94

voltammetry studies, 94

Halides, ion-selective electrodes, 399 Harned cell, 110, 111 Harned's rule, 131, 172, 224

HBis, 18 Henderson equation, 127, 129, 132, 135 Heparin complex, calcium, 240

Heterogeneous membrane electrode, 90,

93, 95, 99, 100, 408

development, 89

preparation, 94

response time, 100 High ionic strengm media, liquid ion exchange membrane electrodes, 415 High ionic strength medium, 358 Human saliva, fluoride, 308 Hydrated glass compositions, 3 Hydrated layer of glass, 314

Hydration energies of ions, 36

Hydration, free energy of, 27 Hydration shell, 7 Hydrochloric acid, activity coefficient, 145 Hydrofluoric acid, 154, 157, 164, 366 Hydrogen chloride levels in gas and aerosol samples, 400 Hydrogen fluoride, 317, 319 Hydroxide interference, fluoride electrode, 157, 417

Hydroxy-apatite, 239

Hyperparathyroidism, 251 Hypercalcemia of cancer, calcium electrode

studies, 269 Hypocalcemic tetany, 234

Hyponatremia, 433

Hysteresis

concentration, 108

temperature, 118, 122, 125,420

In vitro, potentiometric measurements, 294

In vivo

intraluminal pH, 300

potentiometric measurements, 294

Incompletely sealed micropipette electrode, 299

Industrial analysis and control, 349

Industrial analytical instruments, 359

Inert matrix, 90

Inflection point of titration, 416

Infusion of di-sodium EDTA, 252

Insulation techniques, 297

Interaction between double layers, 52

Interferences, electrode, 146, 150, 152, 173, 179, 353

Internal filling solutions, 182

Internal potential, 45, 53

Internal reference electrodes, 109

Intracellular analyses, 296

Intracellular ionic activities, 296

Intracellular pH, 297

Intracellular proteins, 289

Intraluminal pH, 300

Iodide, activity in iodinated proteins, 309

Iodide electrodes, 78, 309, 400

effect of radiation levels, 401

response, 409

Ion activity conventions for, 197

definition of, 61 measurement, 57

standards for, 201

Ion adsorption on electrode surface, 434

Ion-association extraction electrode sys- tems, 409

Ion-binding by organic polyelectrolytes, 297

Ion exchange

equilibrium constant, 2, 3, 6, 18

selectivity, 10

site, 28

Ion-exchange resins, 90

Ion-exchange theory, 97, 98, 104

Ion exchanger, chemical nature, 18 Ion mobility in membrane, 62

Ion-pairing. 147

Ion pairs, neutral, 42

Ion permeation in mitochondria, 7 Ion-sequestering molecules, selectivity of, 1 Ionic activity, 191 , 196

in biological systems, 287

in circulating fluids, 295

intracellular, 296

Ionic complexes, 52
446 INDEX

Ionic strength

buffer, 359, 380, 415

total, 224

Ionized calcium, 216

and serum total calcium, 230, 233, 234, 257

continuous monitoring, 221 pH dependence, 225

protein-bound calcium and diffusible complexes, 270

serum, 217, 254

Ionshydration energies, 36

molecular carriers for, 5

1

Isopotential, 137

Isopotential control, 136

Isothermal intersection point, 137 Isothermenschnittpunkt, 125, 137

Isotherms, selectivity, 30, 34

Kinetic response of fluoride electrode, 154, 155

Kinetics, 330

Kinetic studies, 174, 313

Kinetic study of exchange reaction between

silver EDTA and nickel, 333 Known-increment technique, 381

Lactate, calcium complex, 238 Lanthanum

fluoride membrane, 75, 317

fluoride solubility, 417, 418

hydroxide complexes, 158 response of fluoride electrode, 418

titration of fluoride, 390 Lead electrode, 80, 407, 430, 434 Lead electrode, titration of sulfate, 408 Lead tungstate, 94 Lewis and Sargent equation, 127

Ligands, coordination number of, 32

Limitations of liquid ion exchange membrane electrodes, 415

Limitations of pA measurement, 210

Limiting case of complete dissociation, 5 Limiting case of strong association, 5 Linear null-point potentiometry, 113, 377

Lipid-soluble complexes, 7, 24

Lipid-soluble molecules, 7, 24

Lipophilic ion exchanger molecules, chemical properties of, 16, 18 Liquid exchanger, 6 Liquid ion exchange membrane electrode, 48

in high ionic strength media, 415

limitations, 415

Liquid ion exchangers, selectivity, 1, 10, 26

Liquid junction, 46, 158

cell without, 145 continuous mixture, 128, 133

double, 130

effect of serum, 428

flowing, 128

free diffusion, 128

potential. 111, 112, 123, 127, 149, 159, 161, 182, 194, 211, 212, 242, 244,

290, 375,416

reference electrodes with, 420

residual potential, 194, 242, 244, 290

restrained diffusion, 128

single, 130

Liquid membrane electrodes, 57, 314, 328 complex studies with, 327

mobile sites in, 316

Liquid membrane systems, 61 development of, 64

site in, 63

solvent, 63, 65

theoretical treatment of, 64

Lithium fluoride, 176, 388

Lithium glass electrode, 16 Lithium, titration with fluoride, 176, 388 Maclnnes convention, 197, 208

Macrocyclic antibiotics, 32 Macrocyclic molecules, 1,21

Macrocyclic polyethers, 32

Macrotetrolide electrode, 409 Madelung constant, 30 Magnesium in sea water, 406

Matrix

collodion, 90

inert, 90

paraffin wax, 90

polyethylene, 90

polystyrene, 90

polyvinyl chloride, 90

silicone rubber, 90 Measurements

accuracy of, 355

direct emf, 384

in non-aqueous systems, 422

in vitro, 293, 294

in vivo, 293, 294

surface, 295 Mechanism for cation permeation, 7 Mechanism, selectivity of neutral carrier, 21, 26
INDEX 447

Membrane, 48, 145 Amicon, 428

bilayer, 24

biological, 1, 31, 36, 293

cellophane, 93

collodion, 217

electric conductance, 24

electroneutrality in, 25

fixed-site, 3 1

3

glass cation exchange, 2 ion mobility in, 62

Millipore filter, 63

miscellaneous materials, 94

mixed-precipitate, 434

paraffin, 93, 94

phospholipid bilayer, 7

potential, 2, 8, 42

ultra-thin, 7 Membrane phase, Debye length, 52 Membrane-solution boundary, 40

Mercaptan, 361, 430

Mercury-mercurous

acetate electrode, 123 benzoate electrode, 124

carboxylate electrode, 123

chloride electrode, 1 18 oxalate electrode, 123

picrate electrode, 1 12 propionate electrode, 124 Metal chelates, 90

Metallic electrodes, 306

Methyl sulfide, 361 Methyl tricaprylyl ammonium cation, 409

Microdetermination of fluorine in organic

compounds, 394

Microelectrodes, 287, 296

Micropipette electrode, incompletely sealed, 299

Microtechnique, analate additions potentiometry, 385

Millipore membrane, 63

Mitochondria, ion permeation in, 7

Mitosis, influence of calcium activity, 309 Mixed electrolyte solutions, 287 Mixed ionic solutions, standards, 423

Mixed-precipitate membranes, 434

Mobile sites in liquid membrane electrodes, 316

Mobilities of charged complexes, 53, 54

Mobility

cation, 2, 3 14

MobWity — Continued

dissociated ions, 5

in solid-state membrane systems, 73

ratio, 3, 18, 316

relative, 10 Molecular carriers of ions, 7, 51 Molecules

lipid-soluble, 7, 24

neutral macrocyclic, 8, 2 1 , 23, 24, 5

1

neutral sequestering, 32 Monensin, 18 Monopolar site model, 28, 36 Monovalent cations, electrodes for measuring, 16 Multiple ion-selective electrodes, 364

Multivalent ions, selectivity, 314

Murexide, 217

Muscle, intracellular sodium, 303 N-type glass electrode, 2 N-type non-ideal behavior, 37, 38, 42

Nernst

equation, 59, 150, 163, 222, 353, 375

equation, deviations, 158

factor, 381 Planck equation, 53

potential, 2 Nernstian response, 381 Neutral carriers, 18, 36, 51 mechanism, 21,, 26

selectivity, 10, 21, 26, 27

solubility, 26

theory for, 8

carrier systems, 36

dipole site, 32

macrocyclic antibiotics, 7 macrocyclic molecules, 23, 51

pairs, 6 sequestering molecules, 7, 32 Nickel acetylacetonate dihydrate, 94

Nickel dimethylglyoxime, 93 Nickel electrode, 90, 93

Nigericin, 36 Niobium fluoride complexes, 169

Nitrate content of plants, 398

Nitrate electrode, 397, 409, 412

Nitrate in soil, 398

Nitrilotriacetic acid, chelation of calcium,

185, 328

Nitrobenzene, 16 Nitromethane, 16 Noise, electrode, 430

Nomogram for protein-bound calcium, 261, 265
448 INDEX

Non-aqueous media, 16, 146 Non-aqueous systems

electrode measurements in, 422

reference electrode, 421 Non-flowing biologic systems, 295 Non-zero current, 46

Nonactin, 2 1 , 36 Nonactin homolog electrode, 409

Null-point potentiometry, 376

Null-point potentiometry, linear, 113 Nullpunkt, 125, 137

Oleic acid, 16 On-line analysis, 349

Operational lifetime of continuous systems, 424

Operational pH cell, 1 12 Organic compounds, microdetermination of

fluorine, 394

Organic ions, ion-selective electrodes, 409

Organic polyelectrolytes, 297

Organophilic anion, 4

Origin of membrane potentials, 2 Origin of selectivity, 16 ORP, 361 Orthophenanthroline chelating site group, 72

Osmolality, serum, 433 Osmotic coefficients, 173 Oxalate, electrode response to, 409

Oxidation-reduction

electrodes, 307

equilibria, 143

potential, platinum electrode, 361 Oxygen electrode, 425

p-Ethoxychrysoidine, 95, 103 p-Toluenesulfonate, electrode response to, 409 pA measurement, limitations, 210 pA, operational definition, 193

Paint insulation, 297

Paper and pulp industry, sulfide ion, 361

Paraffin electrode, calcium oxalate, 93 membrane, 93, 94 wax matrix, 90

Parameters, selectivity, 1 Parathormone, 216, 218, 251, 434

Partition coefficient ratio, 6, 26

Partition coefficients, 5, 25, 52, 54

Partition equilibria, 25

Pathologic sera, calcium analysis in, 433

Pattern of selectivity, 28 pCO., 225

Perchlorate electrode, 328, 399, 409

Performance tests for electrodes, 195

Periodate, perchlorate electrode response

to, 399 Permanganate , perchlorate electrode response to, 399

PermselecUve, 42 pH

continuous monitoring, 221

convention, 196 dependence of calcium binding to serum

proteins, 222, 424

dependence of ionized calcium, 225

effect on calcium electrode, 231

intracellular, 297

in vivo, 300

operational cell, 1 12 Phosphate, calcium complex, 224, 238

Phosphate electrode, 101 Phosphate ester systems, 65 Phosphate ion exchanger, 16 Phospholipid bilayer membranes, 7 Phosphoric acid, 16 Phosphoric acid buffer for determination

of fluoride, 153

Physical meaning of selectivity parameters,

10

Physiologic importance of calcium, 216

Physiology, cellular, 296

Planck and Henderson equations, 133 Planck equation, 127 Planck liquid junction, 46

Plants, nitrate content, 398

Platinum electrode, oxidation-reduction

potential, 361 Poisoning by protein, calcium electrode, 244

Poisoning material, 317

Pollution monitoring, 367, 371

Polyelectrolytes

colloidal, 287

ion-binding by, 297

protoplasmic, 290

Polyethers, 1 cyclic, 7, 21 , 36

macrocyclic, 32

Polyethylene matrix, 90

Polysiloxane, 95

Polystyrene matrix, 90

Polysulfides, 430

Polyvinyl chloride matrix, 90

Potassium electrode, 90, 304, 409
INDEX 449

Potassium hexafluorosilicate, 94

Potential

analytical expressions for, 2 asymmetry, 114, 149

bias, 114, 116

biologic membranes, 293

diffusion, 37, 40, 42, 127, 135

drift, 154

electrode, 1 , 191 , 192, 223, 225

equivalence-point, 386

Galvani, 191

gradient, 46

internal, 45, 48, 53

liquid junction. 111, 1 12, 123, 127, 149,

159, 161, 182, 194, 211, 212, 242,

244, 290, 375, 416

Nernst, 2 quasi-steady state, 5

1

reference electrodes, 1 12

residual liquid junction, 194, 242, 244, 290

salt effect, 127

single electrode, 191 standard, 1 12, 114, 116, 123, 126, 137

143, 144, 149

steady-state, 316

streaming, 295, 427

surface, 191 theory of, 1 tip, 291

total, 40, 42

total membrane, 37, 41, 45, 48, 53

Volta, 191

zero, 37, 48, 376, 380, 381

Potentiometric measurements

direct, 375

in vitro, 294

in vivo, 290

Potentiometric titration curves, 386

Potentiometric titrations, 375, 385

advantages, 388

equivalence point, 386

unsymmetrical, 386

Poientiometry, 388

analate additions, 384, 385

direct, 375

linear null-point, 1 1

3

null-point, 376

Precipitation of alkali metal ions with tetraphenylboron, 331

Precipitation of calcium complexes, 239

Precision

direct technique, 376

electrode, 60

titrations, 61 Preparation of heterogeneous membrane

electrodes, 94

Process analysis, 349

Propionate, electrode response to, 409

Protein adsorption on electrode surfaces, 428

binding of ions, 290

calcium-binding by, 222, 243, 247

concentrations, 264

error, 429

extracellular, 289

intracellular, 289

poisoning of electrodes, 244, 290

serum, 222, 226, 234, 257, 259, 271, 282

Protein-bound calcium, 218, 243, 247,

254, 259, 268

and albumin, 261 and diffusible complexes, 270

fractionation, 278 nomogram, 261, 265

Protonation of fluoride, 163 Protoplasmic polyelectrolytes, 290

Pseudo-Nernstian behavior, 144

Quasi-steady state of potential, 51 Quinhydrone electrode, 307 Radioimmunoassay, serum parathormone,

251

Rare-earth fluoride membranes, 75 Rate of diffusion, 52

Rate studies, 316

Ratio

equilibrium constants, 25

formation constants, 26

partition coefficients, 26

Reaction mechanisms, electrode characterization, 340

Reactions, heterogeneous, 331 Reagent addition, differential analysis, 367

Reagent addition to sample stream, 365 Redox electrodes

boride, 94

carbide, 94

graphite, 94

silicide, 94

Reference electrodes, 95, 107, 112, 194

203, 41 1, 412, 413

as bridging electrode, 1 1 1
450 INDEX

Reference eleclrodes— Continued

calomel, 42

1

classification, 108

filling solutions, 42

1

in non-aqueous systems, 421

internal, 109

reproducibility, 108

reversibility of, 108

selection of, 420

stability, 108

stirring effects, 422

temperature hysteresis, 420

use of ion-selective electrodes as, 113 with liquid junction, 420

Relative binding of calcium to albumin and

globulin, 278

Relative mobilities, 10

Relative values for ionized calcium, proteinbound calcium and diffusible complexes, 270

Renal dialysis patients, calcium, 433

Reproducibility of reference electrodes, 108

Residual liquid junction potential, 194, 242,

244, 290

Resins, ion-exchange, 90 Response

electrode, 191, 409

Nernstian, 381

slope, 380, 381

slowing, 317 Response time of electrodes, 100, 183, 295

Restrained diffusion, 128

Reversibility of reference electrodes, 108 Rubber, silicone, 90, 93, 95, 104, 419

Salicylate, electrode response to, 409

Saliva, fluoride in, 308

Salt extraction, 9, 25

Salt effect, potential, 127 Sampling of calcium in blood, 426

Saturated calomel electrode, 112, 113 Sea water

calcium concentration, 397

determination of calcium, 397

divalent cation electrode, measurement of magnesium, 406

fluoride concentration, 384, 393

fluoride to chlorinity ratio, 393

Seal, glass-to-glass, 301

Selectivity, 3, 6, 149, 195 and anionic field strength, 30

coefficient, 353

constant, 69, 97, 99

Se\ectiviXy — Continued

determination by solvent, 5 equilibrium, 27

factors involved, 10, 26, 435

glass electrodes, 30

ion exchanger membranes, 1, 27

isotherms, 30, 34

multivalent ions, 314

neutral carrier membranes, 10, 21, 26, 27

origin, 16 parameter, 1 , 10, 54

pattern, 28

physical meaning, 10

potentiometric, 314

principle, 18

ratios, 98, 100, 144, 183, 436

sequences, 30, 36

Sequestering agents, neutral, 1, 7 Serum

albumin, 234, 257, 274

calcium fractions, 254

calcium in cirrhosis, 253

diffusible calcium complexes, 237

flow rate problems, 427

globulin, 257

ionized calcium, 217, 254

ionized versus total calcium, 230, 233, 234

liquid-junction effect, 428

osmolality, 433

parathormone by radioimmunoassay, 25

1

proteins, 222, 226, 234, 243, 257, 259,

271, 282

total calcium, 234, 235, 236, 257, 268,

274, 281

ultrafiltrate, 235

Shield, driven, 432

Shielding, 431

Silicate interference, fluoride electrode, 150

Silicide electrode, redox, 94

Silicone rubber, 90, 93, 95, 104, 419

Silver, adsorption of, 177

Silver chloride complexes, 146

chloride heterogeneous membrane elec- trode, 95 EDTA and nickel, kinetic study of ex- change reaction, 333

ferrocyanide, 94

halide heterogeneous membrane elec- trode, 95, 99

ion, 177

Silver-silver bromide electrode, 1 17
INDEX 451

Silver-silver— Continued

chloride electrode. 111, 115, 116, 306

iodide electrode, 1 17

sulfide electrode, lOl, 179

Silver sulfide electrode, 77, 177, 179, 324, 402,406,413,434

Silver sulfide-metal sulfide membrane sys- tems, 79

Silver sulfide solubility product, 179

Similarities and differences between solid and liquid exchangers, 7 Single electrode potential, 191

Single ion, 18

activity, 191

acfivity coefficient, 149, 182, 199 conductances, 18

Site group

orthophenanthroline chelating, 72

thio-acid, 72

Site model, monopolar, 28

Sites, 42, 44

chemical properties, 18 concentration, 48

dipolar, 27

electrostadc model, 27

fixed monovalent, 37

free, 48

ion exchange, 28

neutral dipole, 32

transference number, 48

trapped, 36, 50

Size of complexed cafions, 10 Skim milk, determination of calcium, 397

Slope factor compensadon, 136 Slowing of response, 317 Sodium electrode, 173, 202, 205, 366

' Sodium fluoride acfivity coefficient, 161, 171 Sodium, intracellular, 303 Sodium/potassium rafio in cirrhosis, 433

Soil, determinafion of nitrate, 398

Solid and liquid exchangers, similarities and

differences, 7 electrolyte galvanic cell for oxygen in gas

streams, 425

ion exchanger membranes, 1 ion exchangers, 1,2, 10, 26, 37

organic matrix calcium electrode, 185

state electrodes, 57, 105, 308, 430

Solubility, 418 membrane materials, 97

neutral carriers, 26

Solubility product calcium fluoride, 168 calcium sulfate dihydrate, 185 europium fluoride, 166 lanthanum fluoride, 159, 163, 417, 418

silver sulfide, 179

Solufions, standard reference, 201

Solvent extraction electrode systems, 408

Solvent, liquid membrane systems, 65

Solvent, selecfivity determination by, 5 Source of failure in electrodes, 420

Space charge, 25, 37

Specificity test, fluoride electrode, 153 Spike technique, 381

Spinal fluid, calcium, 249

Stability constants of stannous fluoride complexes, 168

Stability of reference electrodes, 108 Standard

addition equation, general form, 383

addition technique, 383, 384, 390

chemical potential, 37, 137

potential, 112, 114, 116, 123, 126, 143, 144, 149

reference solutions, 201

solutions, 148

Standardization frequency for continuous

systems, 425

Standardizafion procedures, 212

Standards

acfivity, 191, 422

biologic, 292

calibrafing, 292

for mixed ionic solutions, 423

metal buffers, 422

Stannous fluoride complexes, 168

Steady-state potenfial, 316

Stirring effects on reference electrode, 422

Stoichiometry of complexes, 21, 319

Streaming potenfial, 295, 427

Strong association, 49

Successive titration of chloride, bromide

and iodide, 401

Sulfate, 430

calcium complex, 238

electrode, 90, 101, 122, 408, 409

ion exchanger, 16

titration with lead, 408

Sulfide electrode, 77, 101, 179, 402, 405, 413,

430

in paper and pulp industry, 361
452 INDEX

Sulfide — Continued

pollution monitoring, 367

reaction with water, 179

Sulfonic acid, 16 Surface

ion adsorption on electrode, 434

measurements, 295

potential, 191 Symmetrical cell, 432 Temperature coefficients, 179, 354, 432 Temperature dependence of calcium binding to serum proteins, 222, 424

Temperature hysteresis, 108, 118, 122,

125, 420

Temperature shifts, methods of minimizing, 432

Tests for electrode performance, 195 Tetany, hypocalcemic, 234 Tetraalkylammonium chloride electrode, 73 Tetraethylammonium perchlorate, 177

Tetrafluoroborate electrode, 398

Tetraphenylarsonium chloride, titration of

perchlorate, 399

Tetraphenylboron, precipitation of alkali metal ions, 33

1

Thalamid electrode, 124 Thallium amalgam-thallous chloride

electrode, 124, 134 THAM buffer, 433 Theory of electrode potentials, 1, 2 Thermodynamic equilibrium, 40 Thermodynamic studies, 143 Thio-acid site group, 72 Thiocyanate electrode, 78, 408, 409

Thiostannate complex formation, 325 Thorium fluoride, 103, 169 Thorium, potentiometric titration of

fluoride, 390, 394

Tip potential, 291 TISAB, 359, 366, 380

Titration cadmium with EDTA, 81 calcium with EDTA, 395, 416

calcium with EGTA, 397

fluoride with lanthanum, 390

fluoride with lanthanum, thorium and

calcium, 390

lithium with fluoride, 388

perchlorate with tetraphenylarsonium

chloride, 399

sulfate with lead, 408

Titrations advantages, potentiometric, 388

chelating, 228

equivalence point, 386

potentiometric, 375, 385

precision, 61 unsymmetrical, 386

Total concentration, complexed species, 383

Total ion concentration, 357

Total ionic strength, 224

Total ionic strength adjustment buffer, 359, 380

Total potential, 37, 40, 53

Total protein, serum, 226, 257

Transition metal ion interferences, fluoride electrode, 150

Transient phenomena, 314

Transport into cerebrospinal fluid active, 249

facilitated, 249

Transference number, 6 Transference number of free sites, 49 Trapped sites, 36, 50

Tributyl phosphate, 94

Trinactin, 21 , 36

Ultrafiltrable calcium, 235, 254

Ultrafiltrates of sera, 226

Ultra-thin membranes, 7 Unsymmetrical potentiometric titrations, 386

Valinomycin, 21 , 36

Velocity of establishing boundary equilibria, 42 Venous stasis, carbon dioxide losses, 426

Vitamin D, 218 Voltammetry studies with graphite im- pregnated electrode, 94

Volta potential, 191 Water hardness measurements, divalent cation electrode, 360, 406 Water systems, fluoride monitoring, 360, 425 Whole blood calcium, 239 Windows, accessibility, 317 Zero point, 137 Zero potential, 376, 380, 381 Zero shift, 137 Zinc chloride activity, 147 Zinc electrode, 90

Zirconia electrolyte, oxygen electrode, 425

t> U.S. GOVERNMENT PRINTING OFFICE : 1969 OL —348-381



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